CURRICULUM VITAE

Personal Information:

Name: Cornel PasnicuMailing Address: The University of Texas at San Antonio

Department of MathematicsCollege of SciencesOne UTSA CircleSan Antonio, TX 78249, U.S.A.

Telephone: (210) 458-4495E-mail: Cornel.Pasnicu@utsa.edu

cpasnicu@gmail.com

Education:

1976 B.A. University of Bucharest, Bucharest, Romania

1977 M.S. University of Bucharest, Bucharest, RomaniaAdvisor: Ciprian Foias

1987 Ph.D. University of Bucharest, Bucharest, RomaniaAdvisor: Dan Voiculescu (Thesis defended under the supervisionof Ion Colojoara)

Title of M.S. Thesis: The Ext Semigroup of Separable C∗-Algebras

Title of Ph.D. Thesis: The Study of Certain Special Classes of OperatorAlgebras

Employment:

October 1980-September 1991: Research Fellow, National Institute forScientific Research (the Institute of Mathematics Simion Stoilow ofthe Romanian Academy), Bucharest, Romania

September 1991-December 1991: Visiting Scholar of the Institute of

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Mathematics University of Copenhagen, Copenhagen, Denmark

February 1992-June 1992: Visiting Associate Professor, Department ofMathematics, University of Toronto, Canada

July 1992-June 1997: Associate Professor, Department of Mathematics,University of Puerto Rico, Rio Piedras Campus, Puerto Rico,U.S.A.

July 1997-July 2011: Full Professor (with tenure), Department ofMathematics, University of Puerto Rico, Rio Piedras Campus,Puerto Rico, U.S.A.

August 17, 2011-present: Full Professor (with tenure), Department ofMathematics, University of Texas at San Antonio, U.S.A.

Research Grants, NSF panel participations and NSERC reviewer:

NSF grant DMS-9401515, 1994-1996.

NSF grant DMS-9622250, 1996-2000.

DEPSCoR (Defense Experimental Program to Stimulate Competitive Re-search) grant from the U.S. Army Research Office, No. DAAD19-00-1-0152,2000-2004 ($352,500).

NSF grant DMS-0101060, 2001-2005 ($77,776).

Member of the NSF Operator Algebras/Operator Theory panel (Arling-ton, VA, January 22-24, 2002) (this panel decided the NSF research awardsin these areas starting in 2002).

FIPI (UPR Institutional Fund for Research), 2005-2007 ($30,000).

Reviewer of a Natural Sciences and Engineering Research Council ofCanada (NSERC) Discovery Grant proposal (December 2009).

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Selected Talks (since 1991):

Before 1991, I have given talks at a number of international mathematicalconferences on Operator Theory and Operator Algebras, held in Timisoara,Bucharest, Predeal and Craiova (Romania).

(Main Speaker) Summer School in Operator Algebras, Copenhagen,Denmark, August 1991.

(Main Speaker) Meeting on Operator Algebras, Røros, Norway,September 1991.

20th Canadian Annual Symposium on Operator Algebras, Calgary,Canada, May 1992.

(Invited Speaker) 3rd International Workshop and Mini Conference inOperator Theory and Evolution Equations, San Juan and Mayaguez,Puerto Rico, March-April 1993.

GPOTS (Great Plains Operator Theory Symposium), Boulder, Colorado,June 1993.

GPOTS (Great Plains Operator Theory Symposium), Lincoln, Nebraska,May 1994.

(Invited Speaker) AMS Meeting (Special Session “Simple C∗-algebras”),Eugene, Oregon, June 1994.

11th Southeastern Analysis Meeting (SEAM XI), Atlanta, Georgia, March1995.

GPOTS (Great Plains Operator Theory Symposium), Cincinnati, Ohio,May 1995.

(Main Speaker) 5th Annual Meeting of the International Workshop inAnalysis and Its Applications (IWAA), Rolla, Missouri, May 1995.

12th Southeastern Analysis Meeting (SEAM XII), Richmond, Virginia,

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March 1996.

(Invited Speaker) Workshop on “C∗-algebras”, Oberwolfach, Germany,April 1996.

GPOTS (Great Plains Operator Theory Symposium), Tempe, Arizona,May 1996.

(Invited Speaker) Annual Meeting of the AMS (Special Session“Noncommutative Geometry and Applications”), San Diego,California, January 1997.

Joint Meeting of the Canadian Operator Algebras Symposium and theGreat Plains Operator Theory Symposium, Kingston, Canada,May 1997.

(Invited Speaker) International Conference on Operator Algebras andOperator Theory Shanghai, China, July 1997.

(Invited Speaker) Canadian Mathematical Society Meeting (SpecialSession “Amenable C∗-a1gebras”), Victoria, Canada, December1997.

GPOTS (Great Plains Operator Theory Symposium), Manhattan, Kansas,May 1998.

17th Conference on Operator Theory, Timisoara, Romania, June 1998.

(Invited Speaker) Annual Meeting of the AMS (Special Session “OperatorAlgebras and Applications”), San Antonio, Texas, January, 1999.

GPOTS (Great Plains Operator Theory Symposium), Ames, Iowa, May1999.

(Invited Speaker) NATO Advanced Research Workshop on “SimpleC∗-algebras and Non-commutative Dynamical Systems”, MSRI(part of the full-year 2000-2001 Program on Operator Algebras

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organized by MSRI), Berkeley, California, September 2000.

17th Southeastern Analysis Meeting (SEAM XVII), Athens, Georgia,March 2001.

(Invited Speaker) Workshop on “C∗-algebras”, Oberwolfach, Germany,December 2001.

GPOTS (Great Plains Operator Theory Symposium), Charlotte, NorthCarolina, May 2002.

GPOTS (Great Plains Operator Theory Symposium), Urbana-Champaign,Illinois, May-June 2003.

(one of the two 1 hour Invited Speakers) Wabash Extramural ModernAnalysis Seminar, Wabash College, Indiana, April 2004.

(Invited Speaker) Workshop on “The structure of amenable systems”,Banff International Research Station (BIRS), Banff, Canada,October-November 2004.

21st Southeastern Analysis Meeting (SEAM XXI), Lexington, Virginia,April 2005.

(Invited Speaker) GPOTS (Great Plains Operator Theory Symposium),Iowa City, Iowa, May 2006.

(Invited Speaker) Workshop on ”Recent Advances in Operator Algebras”,Rome, Italy, November 2006.

(Invited Speaker - 45 minute talk) Workshop on ”Structure of C∗-Algebras”,Fields Institute (part of the Thematic Program on OperatorAlgebras July-December 2007, organized by the Fields Institute),Toronto, Canada, November 2007.

(Invited Speaker - 40 minute talk) AMS Spring Meeting (Special Session”C∗-algebras, subfactors and free probability”), Claremont,

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California, May 2008.

(Invited Speaker - 60 minute talk) ”Workshop on structure of C∗-algebras”,Qinhuangdao, China, September 2009.

Invited (fully paid) participant at the workshop ”The Cuntz semigroup”,the American Institute of Mathematics, Palo Alto, California,November 2009.

Invited participant at the workshop ”Classification of amenable C∗-algebras”,Banff International Research Station (BIRS), Banff, Canada,September 2010.

”Conference on Structure and Classification of C∗-Algebras”, Centre deRecerca Matematica (CRM) (part of the Research Program ”TheCuntz semigroup and the Classification of C∗-Algebras”, February-July 2011, organized by CRM), Bellaterra, Barcelona, Spain,June 2011.

(Invited Speaker - 60 minute talk) ”2012 Operator Algebras Program”,The Research Center for Operator Algebras, East China NormalUniversity, Shanghai, China, May 2012.

(Invited Speaker) ”Operator Algebras, Frames, & UndergraduateResearch: A conference in Honor of the 70th Birthday of David R.Larson”, Texas A&M University, College Station, Texas, July 2012.

(Invited Speaker - 50 minute talk) ”C*-Algebras, Structures, andClassification” (conference organized by Jilin University), Changchun,China, July 2013. This conference celebrated my 60th birthday.

Also, the paper [11] was presented by one of my co-authors in the SpecialSession on C∗-algebras and Noncommutative Topology, at the Annual Meet-ing of the AMS, San Francisco, January, 1991.

Colloquium Lectures and Seminar Talks (since 1988):

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University of Szeged (Hungary, 1988).

University of Copenhagen (Denmark, 1991).

University of Odense (Denmark, 1991).

University of Aarhus (Denmark, 1991).

University of Toronto (Canada, 1992).

Kansas State University, Manhattan (U.S.A., 1992; Colloquium Talk).

University of California at Los Angeles (U.S.A., 1994).

Georgia Institute of Technology, Atlanta (U.S.A., 1995).

University of New Hampshire, Durham (U.S.A., 1997; Colloquium Talk).

University of Pennsylvania, Philadelphia (U.S.A., 1997 and visit in 2004).

Purdue University, West Lafayette (U.S.A., 1997, 2002, 2004 and 2009;Operator Algebras Seminar Talks).

University of Kansas, Lawrence (U.S.A., 1998; Ellis B. StoufferColloquium Talk).

University of Geneva (Switzerland, 1998).

Institute of Mathematics Simion Stoilow of the Romanian Academy,Bucharest (Romania, 1998, 2002, 2005 and 2006; Colloquium Talks).

Texas A&M University, College Station (U.S.A., 1998 and 2012).

University of Texas at San Antonio (U.S.A., 1998, 2002-2003, 2007 and2009; Colloquium Talks).

University of Rome II “Tor Vergata” (Italy, 2002).

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University of Paris VI (France, 2002; two Seminar Talks).

University of Oregon, Eugene (U.S.A., 2003; Colloquium Talk andAnalysis Seminar Talk).

Indiana University Bloomington (U.S.A., 2004).

East Carolina University, Greenville (U.S.A., 2005; Colloquium Talk).

Wayne State University, Detroit (U.S.A., 2007; Colloquium Talk andJoint Analysis/Topology Seminar Talk).

Vanderbilt University, Nashville (U.S.A., 2009; Colloquium Talkand Informal von Neumann Algebras Seminar Talk).

University of Maryland, Baltimore County, Baltimore (U.S.A., 2010;Colloquium Talk).

University of Houston (U.S.A., 2013).

Teaching Experience: (since 1980)

Undergraduate courses

Introduction to Mathematics

Precalculus (Part I and II)

Calculus

Advanced Calculus

Fundaments of Basic Mathematics

Precalculus (MAT 1093)

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Calculus I (MAT 1214)

Foundations of Analysis (MAT 3213)

Real Analysis I (MAT 4213)

Graduate Courses

Operator Theory (Part I and II)

Operator Algebras

Inductive Limit C∗-algebras

Real Analysis (Part I and II)

Functional Analysis (Part II)

Banach Algebras

C∗-algebras

Topology

Coordinator of Calculus, 1994.

Special Awards:

Simion Stoilow Prize of the Romanian Academy for the year 1988.This is one of the generally two-four prizes given annually in Romania

by the Romanian Academy for the best mathematical achievements in thatcountry. In this case, the prize was awarded for my Ph.D. Thesis.

Honorary Member of the Institute of Mathematics Simion Stoilow of theRomanian Academy.

(Elected in March 2005).

National Romanian Bursary for Best Students in Mathematics (1972-

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1977).This is a fellowship awarded to the best mathematics students at the level

of B.S. or M.S.

Other Information:

My biography appeared in:Who’s Who in America, 57th Edition, 2003.Who’s Who in America, 58th Edition, 2004.Who’s Who in the World, 21st Edition, 2004.2000 Outstanding Academics of the 21st Century, 2004, International Bi-

ographical Centre, Cambridge, England.One Thousand Great Americans 2004, International Biographical Centre,

Cambridge, England.Who’s Who in America, 59th Edition, 2005.Who’s Who in the World, 22nd Edition, 2005.Leading Educators of the World 2005, International Biographical Centre,

Cambridge, England.International Educator of the Year 2005, International Biographical Cen-

tre, Cambridge, England.Who’s Who in America, 60th Edition, 2006.Who’s Who in the World, 23rd Edition, 2006.Who’s Who in American Education, 7th Edition, 2006–2007.Who’s Who in Science and Engineering, 9th Edition, 2006–2007.Who’s Who in America, 61st Edition, 2007.Who’s Who in American Education, 8th Edition, 2007–2008.Who’s Who in America, 62nd Edition, 2008.Who’s Who in America, 64th Edition, 2010.

Award for Academic Excellence and Productivity, University of PuertoRico, Rio Piedras Campus, 1998.

Chairman of the Organizing Committee of the Great Plains OperatorTheory Symposium (GPOTS), May 23-27, 2000, San Juan, Puerto Rico(GPOTS is the most important annual meeting in Operator Theory andOperator Algebras in the USA and the largest conference in these areas in

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the world).

Organizer of the Conference “Functional Analysis and Applications: AConference in the Memory of Ioana Cioranescu”, August 15-17, 2003, Uni-versity of Puerto Rico, Rio Piedras Campus, San Juan, Puerto Rico.

Organizer of the ”Workshop on Analysis on Groups”, March 15-19, 2008,University of Puerto Rico, Rio Piedras Campus, San Juan, Puerto Rico.

My paper ”C. Pasnicu: The projection property, Glasg. Math. J., 44(2002), 293-300” was ranked in the Top 10 Most-Read Articles during aMonth for Glasgow Mathematical Journal, as follows:

1st for April 20103rd for June 20104th for March 20105th for July 20108th for September 2011.

Also, the same paper of mine was ranked in the Top 10 Most-Read Arti-cles for the Previous 12 Months for the above journal, as follows:

2nd in April 20113rd in November 20103rd in March 20114th in August 20104th in September 20104th in October 20104th in February 20114th in May 20115th in December 20105th in July 20116th in January 20117th in June 20118th in August 20118th in November 20119th in July 201010th in October 2011.

I was the supervisor of three Master Theses (of: Victor V. Vega, Jose P.

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Aponte and Jose R. Carrion).

Member of the American Mathematical Society (since 1987).

Member of the National Association of Scholars (1998-1999).

Reviewer for Mathematical Reviews.

Referee for the following journals (till 2011):

Proceedings of the London Mathematical Society

Journal of Functional Analysis

Transactions of the American Mathematical Society

Indiana University Mathematics Journal

Commentarii Mathematici Helvetici

Journal of Operator Theory

Journal of Mathematical Analysis and Applications

International Journal of Mathematics

Proceedings of the American Mathematical Society

K-theory

Mathematica Scandinavica

Rocky Mountain Journal of Mathematics

Bulletin Mathematique de la Societe des Sciences Mathematiquesde Roumanie (Nouvelle Serie)

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Birkhauser Verlag

La Revue Roumaine de Mathematiques Pures et Appliquees

Proceedings of the 5th. International Workshop in Analysis andIts Applications, Missouri, 1995

Citations in Research Journals:

I am cited more than 222 times in journals like:

Proceedings of the International Congress of Mathematicians,Switzerland, 1994

Annals of Mathematics

Inventiones Mathematicae

Journal of the American Mathematical Society

Duke Mathematical Journal

Proceedings of the London Mathematical Society

Journal of Functional Analysis

Journal fur die Reine und Angewandte Mathematik

Mathematische Annalen

American Journal of Mathematics

Transactions of the American Mathematical Society

Documenta Mathematica

Annales de l’Institut Fourier Grenoble

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Indiana University Mathematics Journal

Ergodic Theory and Dynamical Systems

International Journal of Mathematics

Journal of Operator Theory

Pacific Journal of Mathematics

Canadian Journal of Mathematics

Communications in Mathematical Physics

K-theory

Mathematische Zeitschrift

Mathematica Scandinavica

Contemporary Mathematics

Citations in Books:

1. S. Stratila and L. Zsido: Lectures on von Neumann algebras, AbacusPress, Tunbridge Wells, Kent, 1979, England.

2. S. C. Power: Limit algebras: an introduction to subalgebras of C∗-algebras, Pitman Research Notes in Mathematics Series, 278, LongmanScientific & Technical, 1992.

3. Ideas and Methods in Mathematical Analysis and Applications: InMemory of Raphael Hoegh-Krohn, Edited by S. Albeverio, J.E. Fen-stad, H. Holden and T. Lindstrøm, Cambridge University Press, 1992.

4. C∗-algebras: 1943-1993: a fifty year celebration: proceedings of anAMS special session held January 13-14, 1993 at the San Antonio Con-vention Center in San Antonio, Texas, Robert S. Doran editor, Con-temporary Mathematics Vol. 167, A.M.S., 1994.

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5. H. Su: On the classification of C∗-algebras of real rank zero: Inductivelimits of matrix algebras over non-Hausdorff graphs, Memoirs of theA.M.S., 1995, Vol. 114, No. 547.

6. H. Lin and N. C. Phillips: Classification of direct limits of even Cuntz-circle algebras, Memoirs of the A.M.S., 1995, Vol. 118, No. 565.

7. L. Li: Classification of Simple C∗-algebras: Inductive Limits of MatrixAlgebras over Trees, Memoirs of the A.M.S., 1997, Vol. 127, No. 605.

8. T. A. Loring: Lifting Solutions to Perturbing Problems in C∗-algebras,Fields Institute Monographs, A.M.S., Providence, Rhode Island, 1997.

9. Operator Algebras and their Applications, Peter A. Fillmore, JamesA. Mingo editors, Fields Institute Communications, A.M.S. Providence,R.I., 1998.

10. M. Rørdam: Classification of Nuclear, Simple C∗-algebras, in “Opera-tor Algebras and Non-Commutative Geometry, Vol. VII: Classificationof Nuclear C∗-algebras. Entropy in Operator Algebras”, Encyclopaediaof Mathematical Sciences 126, Springer Verlag, Heidelberg, 2001.

11. H. Lin: An Introduction to the Classification of Amenable C∗-Algebras,World Scientific Publishing Co., Inc., River Edge, NJ, 2001.

12. B. Blackadar: Operator Algebras: Theory of C∗-Algebras and von Neu-mann Algebras (Encyclopaedia of Mathematical Sciences), SpringerVerlag, 2005.

13. Operator Structures and Dynamical Systems, July 21-25, 2008, LorentzCenter, Leiden, The Netherlands, Satellite Conference of the Fifth Eu-ropean Congress of Mathematics, Marcel de Jeu, Sergei Silvestrov,Christian Skau, Jun Tomiyama Editors, Contemporary Mathematics,Vol. 503, A.M.S, Providence, R.I., 2009, 317 pages.

Service (at the UTSA):

2012 - 2014 The representative of the Department of Mathematics fora two year term on the Graduate Council (September 1, 2012 - May 31, 2014)

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2012 Department of Mathematics PPE Committee (Periodic Perfor-mance Evaluation Committee)

2012 - Present Committee Chair, Department of Mathematics GraduateStudies Committee

2012 - Present Committee Chair, Department of Mathematics Evalua-tion Committee (Research Committee)

2012 - Present Department of Mathematics Graduate Program Commit-tee (Review Subcommittee)

2012 - Present Department of Mathematics PhD Committee

2012 - 2013 Department of Mathematics Search Committee

2012 The author of a Letter of Reference for an applicant to the NationalScience Foundation program: Mathematical Sciences Postdoctoral ResearchFellowships (MSPRF) and of a Letter of Reference posted on the Math-Jobs.Org website of the A.M.S.

2012 Reviewer for Mathematica Scandinavica

2012 Reviewer for Bulletin Mathematique de la Societe des SciencesMathematiques de Roumanie (Nouvelle Serie)

2013 Reviewer for the Bulletin of the London Mathematical Society

2013 The author of a Letter of Reference for an applicant for the Fall2014 term at the University of Texas at Austin

2013 The author of Letters of Reference for an applicant to GraduateSchools and for two applicants to postdoctoral positions

2013 My profile was listed in the AcademicKeys Who’s Who in SciencesHigher Education

2014 The author of a Letter of Reference for an applicant for the Fall

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2014 term at the University of Texas at Austin

Description of Research:

My research work concerns the fields of Functional Analysis, OperatorAlgebras and Algebraic Topology.

In my joint work with C. Foias and D. Voiculescu [1] (see list of publi-cations) a new characterization is given of strongly reductive, commutative,separable algebras of operators. This requires a new characterization of weaklimits of sequences of orthogonal projections, asymptotically invariant withrespect to an algebra of operators. The technique developed here has alsobeen used to obtain interesting results in a different connection.

In [2] we show that in many situations a weighted shift with trace-classself-commutator is a compression modulo the Hilbert-Schmidt class of a nor-mal operator. This result provides an affirmative answer to a particular caseof a conjecture of Voiculescu.

Some of my papers are concerned with the problem, suggested in 1980by E.G. Effros, of studying in a systematic way the C∗-algebra inductivelimits of finite direct sums of matrix algebras over commutative C∗-algebras.(This was of course also suggested by the theory of AF algebras). My paper[3] could be thought as the first attempt to consider this problem. In [3], Iconsidered certain C∗-algebras which are inductive limits of matrix algebrasover the continuous functions on the two dimensional torus. The connectinghomomorphisms were assumed to be compatible with a certain covering mapfrom the two dimensional torus to itself. It is proved that such an induc-tive limit does not depend on the choice of the connecting homomorphisms.Moreover, it is shown that any such C∗-algebra is the tensor product of twoBunce-Deddens algebras. Such kinds of C∗-algebras are completely classifiedmodulo isomorphisms or stable isomorphisms in [4]. This is done in numbertheoretical terms and in terms of K-theoretical invariants.

In [6] we give sufficient conditions (of a cohomological nature) for aninductive limit of finite direct sums of matrix algebras over commutative C∗-algebras to be trivial, i.e., the tensor product of a commutative C∗-algebraand an inductive limit of finite dimensional algebras.

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My paper with M. Dadarlat [7] contains an extension to continuous fieldsof C∗-algebras (or C∗-algebra bundles) of G.A. Elliott’s classification of AFalgebras. We consider inductive limits of finite direct sums of matrix alge-bras over the algebra of continuous functions on a fixed connected space X.We suppose that the connecting homomorphisms are C(X)-linear. Any suchlimit is shown to be isomorphic as a C(X)-module to the C∗-algebra definedby a certain continuous field of AF algebras. For many spaces X, we giveclassification results for such C∗-algebras viewed as C(X)-modules. The in-variants are K-theoretical in nature.

In [8] we consider a discrete group acting in a certain way on a unital C∗-algebra. The group of automorphisms of the corresponding reduced crossedproduct which leave the algebra invariant is described and its homotopygroups are computed, in some commutative situations. The computation isquite specific in the case of Bunce-Deddens algebras and the irrational rota-tion algebras.

In [9] we consider the same situation as above (with the C∗-algebra com-mutative and the group acting on it the integers). It is proved that, undercertain assumptions on the dynamical system, such an automorphism is ap-proximately inner if (and only if) it acts trivially on the K1-group. Ourtheorem generalizes a result of B. Brenken.

In [10] and [11] we consider inductive limits of the same type as before,which are simple and such that the dimensions of the spectra of the buildingblocks in the sequence are bounded. It is proved that, in the unital case, theinvertible elements are dense in the C∗-algebra limit. Using in an essentialway the techniques developed in this paper (in particular, an application ofthe Michael selection theorem), B. Blackadar, Dadarlat and M. Rørdam suc-ceeded in extending an important result of Blackadar, O. Bratteli, Elliott andA. Kumjian concerning the real rank in certain inductive limit C∗-algebras.

In [12] we give some properties of the homomorphisms of Bunce-Deddensalgebras in terms of a canonical uniformly hyperfinite subalgebra of theBunce-Deddens algebra, dense in the trace norm. Results of a similar typeare obtained in [17] but for the automorphisms of some more general induc-tive limit C∗-algebras, including many Goodearl algebras of real rank zero.

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In [13], we prove that any two homomorphisms between two fixed matrixalgebras over the continuous functions on the two dimensional torus whichare compatible with the same covering map from the two-torus to itself areinner equivalent. This result extends the main result in [3]; also, it was one ofthe main tools used by Elliott and G. Gong to prove that certain C∗-algebrainductive limits of finite direct sums of matrix algebras over the continuousfunctions on the two-torus are C∗-algebra inductive limits of finite directsums of matrix algebras over the one-dimensional torus.

In [14] we obtain the same kind of results as in [13], but in a more generalsetting. They extend also some results of Dadarlat.

In [15] we show that a large number of inductive limits in the class sug-gested by Effros have cancellation, and the strict comparability of their pro-jections is completely determined by the tracial states. This is in accordancewith a conjecture of Blackadar.

Let X be a product of spheres and let F ⊆ C(X) be a finite subset.In [16] we prove that any unital homomorphism Φ : C(X) → Mn(C(Y )) ishomotopic to a unital homomorphism Φ′ : C(X) → Mn(C(Y )) such thatΦ′(F ) is approximately contained in a C∗-subalgebra of Mn(C(Y )) of circletype (i.e., a finite direct sum of matrix algebras over C(S1) or a quotientof C(S1)), provided that n/(dim(Y ) + 1) is large enough. We prove also aclassification result for simple, real rank zero inductive limits of finite directsums of matrix algebras over C(S2) and C(S1×S1) (showing first that theyare in fact inductive limits of circle algebras).

In [18] we determine all the possible values of the sets τ({p ∈ A|p = p∗ =p2}) and respectively τ∗(K0(A)) for large classes of unital, separable, simpleC∗-algebras with real rank zero, where τ is a (quasi)trace of A.

In [19] we prove that “many” unital AH algebras (which may not be ofreal rank zero) have cancellation, that the strict comparability of their pro-jections is decided by the tracial states and that their K0-group is weaklyunperforated in the sense of Elliott. These results give new particular affir-mative answers to a conjecture of Blackadar. A new characterization of theAH algebras of real rank zero and with the dimensions of their local spectra

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uniformly bounded (≤ 3) is given.

Let X = Sn1×Sn2× . . .×Snk or let X be a compact absolute retract. Weshow in [20] that if a monomorphism Φ : C(X)→ A is homotopically trivial,then Φ can be approximated pointwise by homomorphisms from C(X) to Awith finite dimensional range, provided that A belongs to a certain class ofsimple C∗-algebras of real rank zero. These C∗-algebras include all purelyinfinite simple C∗-algebras, the Bunce-Deddens algebras and the irrationalrotation algebras. In particular, this generalizes a crucial result in the Brown-Douglas-Fillmore theory. It is also shown that if A is a simple C∗-a1gebraof the form A = lim

→C(Xk,Mnk

), where each Xk is a compact contractible

metric space and if A has real rank zero, then A is an AF algebra (in fact,a more general result is proved).

In [21], [22], [24] we give several necessary and sufficient conditions foran AH algebra to have its ideals generated by their projections. Denote byC the class of AH algebras as above and in addition with slow dimensiongrowth. We completely classify the algebras in C up to a shape equivalenceby a K-theoretical invariant. For this, we show first, in particular, that anyC∗-algebra in C is shape equivalent to an AH algebra with slow dimensiongrowth and real rank zero (generalizing so a result of Elliott-Gong). Weprove that any AH algebra in C has stable rank one (i.e., in the unital case,that the set of the invertible elements is dense in the algebra), generalizingresults of Blackadar-Dadarlat-Rørdam and of Elliott-Gong. Other nonstableK-theoretical results for C∗-algebras in C are also proved.

In [23] we show that if we have an exact sequence of AH algebras 0 →I → A→ B → 0, then A has the ideal property (i.e. any ideal is generatedby its projections) if and only if I and B have the ideal property. Also, weprove that an extension of two AH algebras with the ideal property which areinductive limits of circle algebras is an AH algebra with the ideal propertywhich can be written as an inductive limit of circle algebras if and only if theextension is quasidiagonal.

In [25] we answer - jointly with Dadarlat - a question of Pedersen provingthat the ideal property doesn’t pass to extensions. We describe the idealstructure of an AH algebra (in fact we prove a more general theorem) gener-

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alizing so a result of Elliott. We study the behaviour of the AH algebras withthe ideal property with respect to stable isomorphism and also we prove thatfor any AH algebra A with slow dimension growth and the ideal propertythe projections in M∞(A) have the Riesz decomposition and interpolationproperties and K0(A) is a Riesz group.

In [26] we prove that the ideal property is not preserved under minimaltensor products (even in the separable case).

In [27] we prove some results concerning the behavior of the (strong)GAH algebras with respect to extensions, the ideal property, stable isomor-phism and hereditary C∗-subalgebras. Some of our results in [25] about AHalgebras are generalized.

In [28] we prove a characterization of the ideal property for a large classof C∗-algebras in terms of vanishing conditions for the finite traces on thealgebra. An application of this result to a class of GAH algebras is also given.

In [29] we extend some of our results concerning characterizations of theideal property, extensions and ideal structure to a more general class of C∗-algebras (inductive limits of finite direct sums of unital C∗-algebras whoseproper ideals have no nonzero projections).

In [30] we prove that the ideal property and the projection property donot coincide in general even in the separable case (despite of the fact that, aswe proved before, they are the same for GAH algebras - and, in particular,for AH algebras - and for separable LB algebras). We also study the behav-ior of the projection property with respect to several natural operations.

In [31], we describe the lattice of the ideals generated by projections andwe prove a characterization of the ideal property for “large” classes of crossedproducts of commutative C∗-algebras by discrete, amenable groups; some ap-plications are also given. We answer a question of Shuzhou Wang, showingthat there are crossed products of C∗-algebras with the ideal property bygroups with the ideal property which don’t have the ideal property.

In [32] we introduce some classes of C∗-algebras with “good” local ap-proximation properties - the LB algebras and several subclasses of them -

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which generalize, among others, the AH algebras, the AD algebras and theseparable, simple C∗-algebras with an approximate unit of projections. Weinitiate the study of these new and rich classes of C∗-algebras, proving re-sults about the ideal property, real rank zero, the projection property, idealstructure, inductive limits, stable isomorphism, hereditary C∗-subalgebrasand extensions. Some of our previous results about AH algebras and GAHalgebras are generalized.

In [33], we prove that in “many” interesting cases, the minimal tensorproduct of two non-zero C∗-algebras A and B has the ideal property if andonly if A and B have the ideal property (note that this is not always true).We also obtain several characterizations of the non-zero, unital, commutativeC∗-algebras with the ideal property.

In [34], we give a necessary and sufficient condition for the C∗-algebraassociated to an arbitrary continuous field of C∗-algebras to have real rankzero. Some applications of this result are given, including a characterizationof the real rank zero property for the C∗-algebras with Hausdorff primitivespectrum.

In [35], we study - jointly with Dadarlat - the separable C∗-algebras asso-ciated to continuous fields over locally compact metrisable zero dimensionalspaces whose fibers are Kirchberg algebras satisfying the UCT. We show thatthese algebras are inductive limits of finite direct sums of Kirchberg algebrasand they are classified up to isomorphism by topological invariants.

Let A be the C∗-algebra associated to an arbitrary continuous field of C∗-algebras. In [36] we give a necessary and sufficient condition for A to havethe ideal property and, if moreover A is separable, we give a necessary andsufficient condition for A to have the projection property. Some applicationsof these results are given. We also prove that “many” crossed products ofcommutative C∗-algebras by discrete, amenable groups have the projectionproperty, generalizing some of our previous results.

In [37] we show - jointly with Rørdam - that a separable purely infiniteC∗-algebra is of real rank zero if and only if its primitive ideal space has abasis consisting of compact-open sets and the natural map K0(I)→ K0(I/J)is surjective for all closed two-sided ideals J ⊂ I in the C∗-algebra. It follows

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in particular that if A is any separable C∗-algebra , then A ⊗ O2 is of realrank zero if and only if the primitive ideal space of A has a basis of compact-open sets, which again happens if and only if A⊗O2 has the ideal property.Our main theorem strongly generalizes a result of Perera-Rørdam (J. Funct.Anal. 2004) and, in the separable case, a result of Zhang.

In [38] we introduce - jointly with Carrion - several classes of C∗-algebras(using for this local approximations by ”nice” C∗-algebras), that generalizethe AH algebras, among others. We initiate their study, proving mainly re-sults about the ideal property, but also about the ideals generated by theirprojections, the real rank zero, the weak projection property, minimal tensorproducts, extensions, quasidiagonal extensions, ideal structure, the largestideal with the ideal property and short exact sequences. Some of my previ-ous results are generalized.

Let D be a strongly self-absorbing, K1-injective C∗-algebra (e.g., theJiang-Su algebra Z and O∞). In [39] we characterize, in particular, whenA ⊗ D has the ideal property, where A is a separable, purely infinite C∗-algebra. Answering a natural question, we prove that there is a separable,nuclear C∗-algebra B such that RR(B) = RR(B ⊗Z) = sr(B) = sr(B ⊗Z)= 1 and Prim(B) has two elements (in particular, Prim(B) has a basis con-sisting of compact-open sets) but B ⊗ Z does not have the ideal property.We also discuss permanence properties for some large classes of separable,D-stable C∗-algebras with the ideal property. For a separable C∗-algebra Cwe analyze whether the property RR(C ⊗ Z) = 0 implies or is implied bythe property RR(C ⊗ O∞) = 0, and we show that they are equivalent for”many” separable C∗-algebras C.

In [40] we prove - jointly with Gong, Jiang and Li - that if A is an AHalgebra with the ideal property and with very slow dimension growth suchthat K∗(A) is torsion free, then A is the inductive limit of a sequence of finitedirect sums of matrix algebras over C(S1).

In [41] we prove - jointly with Gong, Jiang and Li - that if A is an AHalgebra with the ideal property and with very slow dimension growth, thenA is in fact an AH algebra over (special) base spaces of dimensions at most 3.

In [42] we define - jointly with Perera - a Riesz type interpolation prop-

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erty for the Cuntz semigroup of a C∗-algebra and prove it is satisfied by theCuntz semigroup of every C∗-algebra with the ideal property. Related to this,we obtain two characterizations of the ideal property in terms of the Cuntzsemigroup of the C∗-algebra. Some additional characterizations are provedin the special case of the stable, purely infinite C∗-algebras, and two of themare expressed in language of the Cuntz semigroup. We introduce a notionof comparison of positive elements for every unital C∗-algebra that has (nor-malized) quasitraces. We prove that large classes of C∗-algebras (includinglarge classes of AH algebras) with the ideal property have this comparisonproperty.

Let α be an action of a finite group G on a C∗-algebra A. In [43] wepresent - jointly with Phillips - some conditions under which properties ofA pass to the crossed product C∗(G,A, α) or the fixed point algebra Aα.We mostly consider the ideal property, the projection property, topologicaldimension zero, and pure infiniteness. In many of our results, additional con-ditions are necessary on the group, the algebra, or the action. Sometimes theaction must be strongly pointwise outer, and in a few results it must have theRokhlin property. When G is finite abelian, we prove that crossed productsand fixed point algebras by G preserve topological dimension zero with nocondition on the action. We give an example to show that the ideal propertyand the projection property do not pass to fixed point algebras (even whenthe group is Z2). The construction also gives an example of a C∗-algebra Bwhich does not have the ideal property but such that M2(B) does have theideal property; in fact, M2(B) has the projection property.

In [44] we define - jointly with Phillips - spectral freeness for actions ofdiscrete groups on C∗-algebras. We relate spectral freeness to other freenessconditions; an example result is that for an action of a finite group, spectralfreeness is equivalent to strong pointwise outerness, and also to the condi-tion that the strong Connes spectrum of the action of the integers generatedby a nontrivial group element is always nontrivial. We then prove perma-nence results for reduced crossed products by exact spectrally free actions,for crossed products by arbitrary actions of the two element group, and forextensions, direct limits, stable isomorphism, and several related construc-tions, for the following properties: 1) The combination of pure infinitenessand the ideal property; 2) Residual hereditary infiniteness (closely related topure infiniteness); 3) Residual (SP) (a strengthening of Property (SP) suit-

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able for nonsimple C∗-algebras); 4) The weak ideal property (closely relatedto the ideal property). For the weak ideal property, we can allow arbitrarycrossed products by any finite abelian group. These properties of C∗-algebrasare shown to have formulations of the same general type, allowing them allto be handled using a common set of theorems.

List of Publications

1. C. Foias, C. Pasnicu and D. Voiculescu: Weak limits of almost invariantprojections, J. Operator Theory, 2 (1979), 79-93.

2. C. Pasnicu: Weighted shifts as direct summands mod C2 of normaloperators, Operator Theory: Advances and Applications, Vol. 11,Birkhauser Verlag, Basel (1983), 275-281.

3. C. Pasnicu: On certain inductive limit C∗-algebras, Indiana Univ.Math. J., 35 (1986), 269-288.

4. C. Pasnicu: Tensor products of Bunce-Deddens algebras, OperatorTheory: Advances and Applications, Vol. 24, Birkhauser Verlag, Basel(1987), 283-288.

5. C. Pasnicu: Studiul unor clase speciale de algebre de operatori, Stud.Cerc. Mat., Tom 40, Nr. 3 (1988), 175-231.

6. C. Pasnicu: On inductive limits of certain C∗-algebras of the formC(X)⊗ F , Trans. Amer. Math. Soc., 310 (1988), 703-714.

7. M. Dadarlat and C. Pasnicu: Inductive limits of C(X)-modules andcontinuous fields of AF -algebras , J. Funct. Anal. 85 (1989), 103-116.

8. M. Dadarlat and C. Pasnicu: On certain automorphisms of reducedcroossed products with discrete groups, J. Operator Theory, 23 (1990),179-193.

9. M. Dadarlat and C. Pasnicu: On approximately inner automorphismsof certain crossed product C∗-algebras, Proc. Amer. Math. Soc., 110(1990), 383-385.

10. M. Dadarlat, G. Nagy, A. Nemethi and C. Pasnicu: Reduction du rangstable topologique dans C∗-algebres limites inductives, C.R. Acad. Sci.,Paris, tome 312, Serie I (1991), 107-108.

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11. M. Dadarlat, G. Nagy, A. Nemethi and C. Pasnicu: Reduction of topo-logical stable rank in inductive limits of C∗-algebras, Pacific J. Math.,Vol. 153, No. 2 (1992), 267-276.

12. C. Pasnicu: Homomorphisms of Bunce-Deddens algebras, Pacific J.Math., Vol. 155, No. 1 (1992), 157-167.

13. C. Pasnicu: Homomorphisms compatible with covering maps of thetwo-torus, C. R. Math. Rep. Acad. Sci. Canada, Vol. XIV, No. 4,August (1992), 143-147.

14. C. Pasnicu: Homomorphisms compatible with some covering maps,C.R. Math. Rep. Acad. Sci. Canada, Vol. XIV, No. 6, December(1992), 263-267.

15. M. Martin and C. Pasnicu: Some comparability results in inductivelimit C∗-algebras, J. Operator Theory, 30 (1993), 137-147.

16. G. A. Elliott, G. Gong, H. Lin and C. Pasnicu: Homomorphisms, homo-topies and approximations by circle algebras, C.R. Math. Rep. Acad.Sci. Canada, Vol. XVI (1994), 45-50.

17. C. Pasnicu: Automorphisms of inductive limit C∗-algebras, Math. Scand.,74 (1994), 263-270.

18. C. Pasnicu: On the range of traces on the set of projections of somesimple C∗-algebras with real rank zero, Stud. Cerc. Mat. (Mathemat-ical Reports), Vol. 47, 5-6 (1995), 453-457.

19. C. Pasnicu: Nonstable K-theory results for some AH algebras, Math.Scand., 78 (1996), 112-120.

20. G. A. Elliott, G. Gong, H. Lin and C. Pasnicu: Abelian C∗-subalgebrasof C∗-algebras of real rank zero and inductive limit C∗-algebras, DukeMath. J., Vol. 85, 3 (1996), 511-554.

21. C. Pasnicu: On some classes of amenable C∗-algebras, Proceedingsof the 5th International Workshop in Analysis and Its Applications,Rolla, Missouri, 1995, Mathematica Moravica, Special Issue, publishedby University of Kragujevac, Yugoslavia, (1997), 251-258.

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22. C. Pasnicu: AH algebras with the ideal property, Operator Algebrasand Operator Theory, Contemporary Mathematics, Vol. 228, A.M.S.,Providence, Rhode Island (1998), 277-288.

23. C. Pasnicu: Extensions of AH algebras with the ideal property, Proc.Edinburgh Math. Soc., 42 (1999), 65-76.

24. C. Pasnicu: Shape equivalance, nonstable K-theory and AH algebras,Pacific J. Math., Vol. 192 (1) (2000), 159-182.

25. C. Pasnicu: On the AH algebras with the ideal property, J. OperatorTheory 43 (2) (2000), 389-407.

26. C. Pasnicu and M. Rørdam: Tensor products of C∗-algebras with theideal property, J. Funct. Anal., 177 (2000), 130-137.

27. C. Pasnicu: On the (strong) GAH algebras, Rev. Roumaine Math.Pures Appl., Vol. 46, No. 4 (2001), 489-498.

28. C. Pasnicu: The ideal property and traces, Math. Nachr., Vol. 227, 1(2001), 127-132.

29. C. Pasnicu: Ideals generated by projections and inductive limit C∗-algebras, Rocky Mountain J. Math., Vol. 31, No. 3 (2001), 1083-1095.

30. C. Pasnicu: The projection property, Glasg. Math. J., 44 (2002),293-300.

31. C. Pasnicu: The ideal property in crossed products, Proc. Amer. Math.Soc., 131, No. 7 (2003), 2103-2108.

32. C. Pasnicu: LB algebras, J. Operator Theory, 50 (2) (2003), 263-281.

33. C. Pasnicu: The ideal property and tensor products of C∗-algebras,Rev. Roumaine Math. Pures Appl., Vol. 49, No. 2 (2004), 153-163.

34. C. Pasnicu: Real rank zero and continuous fields of C∗-algebras, Bull.Math. Soc. Sci. Math. Roumanie (N.S. ), Tome 48 (96), No. 3 (2005),319-325.

35. M. Dadarlat and C. Pasnicu: Continuous fields of Kirchberg C∗-algebras,J. Funct. Anal., 226 (2005), 429-451.

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36. C. Pasnicu: The ideal property, the projection property, continuousfields and crossed products, J. Math. Anal. Appl., 323 (2006), 1213-1224.

37. C. Pasnicu and M. Rørdam: Purely infinite C∗-algebras of real rankzero, J. Reine Angew. Math., 613 (2007), 51-73.

38. J. R. Carrion and C. Pasnicu : Approximations of C∗-algebras and theideal property, J. Math. Anal. Appl., 338 (2008), 925-945.

39. C. Pasnicu: D-stable C∗-algebras, the ideal property and real rankzero, Bull. Math. Soc. Sci. Math. Roumanie (N.S. ), Tome 52 (100),No. 2 (2009), 177-192.

40. G. Gong, C. Jiang, L. Li and C. Pasnicu: AT structure of AH algebraswith the ideal property and torsion free K-theory, J. Funct. Anal., 258(2010), 2119-2143.

41. G. Gong, C. Jiang, L. Li and C. Pasnicu: A reduction theorem for AHalgebras with the ideal property, preprint.

42. C. Pasnicu and F. Perera: The Cuntz semigroup, a Riesz type inter-polation property, comparison and the ideal property, Publ. Mat., 57(2013), 359-377.

43. C. Pasnicu and N. C. Phillips: Permanence properties for crossed prod-ucts and fixed point algebras of finite groups, Trans. Amer. Math.Soc., to appear.

44. C. Pasnicu and N. C. Phillips: Crossed products by spectrally freeactions, preprint arXiv:1308.4921.

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