OT2: Operator Theory: Advances and Applications Vol. 2

Edited by

I. Gohberg

Editorial Board

K. Clancey L. Coburn R. Douglas H.Dym A. Dynin P. Fillmore C. Foias P. Fuhrman S. Goldberg

B. Gramsch W. Helton D. Herrero M. Kaashoek T. Kailath H. Kaper S. Kuroda P. Lancaster L. Lerer

Honorary and Advisory Editorial Board

P. Halmos T. Kato S. Mikhlin

R. Phillips B. Sz.-Nagy

Editorial Office

Department of Mathematics Tel-Aviv University Ramat-Aviv (Israel)

Springer Basel AG

M. Livsic E. Meister B. Mityagin J. Pincus M. Rosenblum J. Rovnjak D. Sarason H. Widon D. Xia

1bpics in Modem Operator Theory 5th International Conference on Operator Theory, Timisoara and Herculane (Romania), June 2-12, 1980

1981

Volume Editors

C.Apostol R. G. Douglas B. Sz.-Nagy D. Voiculescu

Managing Editor

Gr. Arsene

Springer Basel AG

Volume Editorial Office

Department of Mathematics INCREST Bd. Pacii 220 79622 Bucharest (Romania)

CIP-Kurztitelaufnahme der Deutschen Bibliothek

Topics in modern operator theory / 5th Internat. Conference on Operator Theory, Timisoara and Herculane (Romania), June 2-12,1980. Vol. ed. C. Apostol... Co-ed. Gr. Arsène. - Basel ; Boston ; Stuttgart : Birkhäuser, 1981.

(Operator theory ; Vol. 2) ISBN 978-3-7643-1244-2

NE: Apostol, Constantin [Hrsg.]; International Conference on Operator Theory (05,1980, Timisoara; Herculane) ; GT

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner.

© Springer Basel AG 1981 Originally published by Birkhäuser Verlag Basel in 1981 Softcover reprint of the hardcover 1st edition 1981

ISBN 978-3-7643-1244-2 ISBN 978-3-0348-5456-6 (eBook) DOI 10.1007/978-3-0348-5456-6

ALBRECHT, E.

ANDERSON, J.

APOSTOL, C.; MARTIN, M.

CIORANESCU, I.

DOUGLAS, R.G.

DUPRE:, M.; FILLMORE, P.

ECKSTEIN, G.

FIALKOW, L.

GILFEATHER, F.L.; LARSON, D.R.

GOHBERG, I.; KAASHOEK, M.A.; VAN SCHAGEN, F.

CONTENTS

Preface 7

List of participants ..••••••....••••. 9

Program of the conference •••••••.•••• 12

On closed operator alqebras generated by analytic functional calculi •••••••...••.•.•••..•.•••.•.•• 17

A conjecture concerning the pure states of B(H) and a related theorem .•.•••••••..•..••.•.••••.••••. 27

A C*-algebra approach to the Cowen-Douglas theory ...••.••••••...•• 45

On periodic distribution groups 53

On the smoothness of elements of Ext ......•••••.•...•••..••..•••..•. 63

Triviality theorems for Hilbert modules •.•••.•.••..••..••..•..••••••• 71

Exact controllability and spec-trum assignment •.•..•..•••.••.•.•.••. 81

Generalized derivations •....•....•... 95

Commutants modulo the compact operators of certain CSL algebras ..•.••••••.•••.•••••..•.•••.• 105

Similarity of operator blocks and canonical forms. II: Infi­nite dimensional case and Wiener-Hopf factorization ••.•..•.••.• 121

CONTENTS

HERRERO, D.A.

JONES, V.F.R.

NAGY, B.

NIKOLSKII, N.K.

OCNEANU, A.

PELIGRAD, C.

PIMSNER, M.; POPA, S.; VOICULESCU, D.

SUCIU, I.

SUCIU , N.; VALU9ESCU, I.

VOICULESCU, D.

WILLIAMS, J.P.

Unitary orbits of power partial isometries and approximation by block-diagonal nilpotents •.••..•••••• 171

Isomorphisms of the automorphism groups of type II factors ........•.•. 211

The spectral residuum for each closed opera tor •.•••••.••.••••.•.•••• 221

Two applications of Hankel operators .••.•••..••.••••..••.••••••. 239

A Rohlin type theorem for qroups on von Neumann algebras ....••• 247

Derivations of C*-alqebras which are invariant under an automorphism group ••.••...•.•••.••.•• 259

Remarks on ideals of the Calkin­-algebra for certain singular extensions .•.•..•.••.•..•...•...•••.. 269

Modelling by L2-bounded analytic functions ...•.••.••.•••••.••..•••.••• 279

The maximal function of doubly commuting contractions •.............. 295

Remarks on Hilbert-Schmidt perturbations of almost normal operators ••••..••.•.••••••..•••••.••. 311

Derivation ranges: open problems ....• 319

Problem list •.••••••.••••.•••.•••••.• 329

6

PREFACE

The first of the annual Operator Theory conferences in Ti­

mi~oara held four years ago was a meeting of operator theory spe­

cialists from the National Institute for Scientific and Techni­

cal Creation in Bucharest and from the University of Timi~oara.

Since then, the participation to these conferences has greatly

increased, by being attended first by operator theorists from

allover the country and (since 1978) by an increasing number of

foreign mathematicians. Thus the 1980 Conference can be regarded

as a truly international Operator Theory meeting, fifteen coun­

tries being represented at it.

These conferences are conceived as a means to promote the

cooperation between specialists in all areas of Operator Theory.

Among the main topics in 1980 were: dilation theory, invariant

subspaces, connections with the theory of cX-algebras, subnormal

operators, multidimensional functional calculus etc. Though not

included in this volume, we would like to mention that in 1980

some special sessions concerning other fields of Functional Ana­

lysis were organized at the Operator Theory conference.

The research contracts of the Department of Mathematics of

INCREST with the National Council for Sciences and Technoloa,y of

Romania provided the means for developping the research activi­

ty in Functional Analysis; these contracts constitute the gene­

rous framework for these meetings.

We want also to acknowledge the support of INCREST and the

excelent organizing job done by our host - University of Timi­

~oara -. Professor Dumitru Ga~par and Professor Mircea Reghi~

are among those people in Timi~oara who contributed in an essen­

tial way to the success of the meeting.

We are indebted to Professor Israel Gohberg for including

these Proceedings in the OT Series and for valuable help in the

editing process. Birkhauser Verlag was very cooperative in pu-

PREFACE 8

blishing this volume.

Rodica Gervescu and Camelia Minculescu dealt with the dif­

ficult task of typing the whole manuscript; they did an exce­

lent job in a very short time.

Organizing Committee

Head of Math.Department Organizers, of INCREST,

Zoia Ceau§lescu Constantin Apostol

Dan Voiculescu

September 1980

LIST OF PARTICIPANTS*)

ALBRECHT, Ernst ALBU, Adrian ANDERSON, Joel ANDO, Tsuyoshi APOSTOL, Constantin ARSENE, Grigore BABESCU, Gheorghe BACALU, loan BALINT, Stefan BANULESCU, Martha B~NZARU, Titus BARTLE, Robert BERECHET, Oprea BOBOC, Nicu BOC$A, Minerva BlAAU$, Silviu BORO~, Emil BUeUR, Gheorghe BURLACU, Eugen CALIANU, Rodica CAMPU, Eugen CEAU~ESCU, Zoia CEAU9U, Traian CHARLES, Bernard CHARLES, Josette CHEVREAU, Bernard CIORANESCU, Ioana COFAN, Nicolae CONSTANTIN, Gheorghe CONSTANTINESCU, Tiberiu COSTINESCU, Roxana CRAIOVEANU, Mircea CRSTICI, Boris DANET, Nicoale DELCZEG, Adriana DEUTSCH, Emerich DINESCU, Gabriela 017'11., Petre DOGARU, Octavian DOUGLAS, Ronald G. DRAGOMIR, Achim DRAGOMIR, Paraschiva

University of Saarlandes, West Germany University of Timi~oara Pennsylvania State University, USA Hokkaido University, Japan INCREST, Bucharest INCREST, Bucharest Politechnical Institute, Timi$oara Politechnical Institute, Bucharest University of Timi~oara University of Bucharest Politechnical Institute, Timi~oara University of Illinois, USA INCREST, Bucharest University of Bucharest University of Timi~oara University of Timi$oara University of Timi~oara INCREST, Bucharest Politechnical. Institute, Timi~oara Politechnical Institute, Bucharest University of Bucharest INCREST, Bucharest Politechnical Institute, Timi~oara University of Montpellier, France University of Montpellier, France INCREST, Bucharest INCREST, Bucharest Politechnical Institute, Timi$oara University of Timi$oara INCREST, Bucharest University of Bucharest University of Timi$oara Politechnical Institute, Timi$oara Politechnical Institute, Bucharest University of Timi$oara Politechnical Institute of New York,USA University of Bucharest Central Institute of Physics, Bucharest University of Timi90ara State University of New York, USA University of Timi$oara University of Timi~oara

*)Romanian participants are listed only with the name of their institution.

LIST OF PARTICIPANTS

DRECIN, Gheorghe DURSZT, Endre ECKSTEIN, Gheorghe FIALKOW, Larry FILLMORE, Peter A. FRUNZA, ~tefan FUGLEDE, Bent GALETAR, Elisabeta GANDAC, Florea GA~PAR, Dumitru GAVRUTA, Pa~c GEORGESCU, Horia GEORGESCU, Vladimir GILFEATHER, Frank L. GODINI, Gliceria GOLOGAN, Radu-Nicolae GROSU, Cor ina GRZYBOWSKI, Henryk T. GUSSI, Gheorghe HERRERO, Domingo A. HIRI~, Viorel HO SI HAU ISTRATESCU, Ioana JONES, VAUGHAM R.F. KE:RCHY, Lasz16 LIPOVAN, Octavian LU, Shijie MARTIN, Mircea MARU9TER , ~tefan MEGAN, Mihail MENNICKEN, Reinhard MIEL, George MIHALACHE, Georgeta MIHALACHE, Nicolae MINEA, Gheorghe MOLDOVEANU, Emil NAGY, BcHa NEAGU, Mihai NICULESCU, Constantin NIKOLSKII, Nikolai K. OBADEANU, Virgil OCNEANU, Adrian OLIN, Robert F. PAPUC, Dan PASNICU, Cornel PAUNESCU, Doru PELIGRAD, Costel PELIGRAD, Magda PETZ, Denes PIMSNER, Mihai POPA, Constantin POPA, Eugen POPA, Nicolae POPA, Sorin

University of Timi90ara University of Szeged, Hungary University of Timi90ara Western Michigan University, USA Dalhousie University, Canada University of Iagi University of Copenhagen, Denmark University of Timigoara Politechnical Institute, Bucharest University of Timigoara Politechnical Institute, Timigoara University of Bucharest

10

Central Institute of Physics, Bucharest University of Nebraska, USA INCREST, Bucharest INCREST, Bucharest CIMIC, Bucharest University of Gliwice, Poland INCREST, Bucharest IVIC, Venezuela University of Timigoara University of Hanoi, Vietnam Politechnical Institute, Timigoara University of Geneva, Switzerland University of Szeged, Hungary Politechnical Institute, Timigoara Universityof Nankin,People's Republic of China INCREST, Bucharest University of Timi~oara University of Timieoara Regensburg University, West Germany University of Nevada, USA INCREST, Bucharest INCREST, Bucharest INCREST, Bucharest TLHS, Bucharest Budapest Technological University,Htmgary Politechnical Institute, Timigoara University of Craiova Steklov Institute Leningrad, USSR University of Timigoara INCREST, Bucharest Virginia State University, USA University of Timigoara INCREST, Bucharest University of Timigoara INCREST, Bucharest Center of Mathematical Statistics,Bucharesti Mathematical Institut,Budapest, Hungary INCREST, Bucharest University of Timigoara University of Iagi INCREST, Bucharest INCREST, Bucharest

LIST OF PARTICIPANTS

POPESCU, Nicolae POTRA, Florian A. PREDA, Petre PUTINAR, Mihai RADU, Viorel REGHI9, Mircea REGHI9, Monica RO~;U, Radu ~ABAC, Mihai SCHMtiDGEN, Konrad SETELECAN, Alexandru SINGER, Ivan STAN, Ilie STANA9ILA, Octavian STANCU, Dimitrie D. STANCU, Felicia STEPAN, Aurel STOICA, Lucretiu STRATILA, ~erban SUCIU, loan SUCIU, Nicolae SZ~KEFALVI-NAGY, Bela TELEMAN, Silviu· TEODORESCU, Radu TERESCENCO, Alexandru TIMOTIN, Dan TOPUZU, Elena TOPUZU, Paul TROIE, Valeriu TUDOR, Constantin VALU~ESCU, Ilie VASILESCU, Florian H. VOICULESCU, Dan VUZA, Dan WILLIAMS, JAMES P. ZOPOTA, Nicolae

University of Timi 90ara INCREST, Bucharest University of Timi 90ara INCREST, Bucharest University of Timi90ara University of Timigoara University of Timi90ara University of Bucharest University of Bucharest Karl Marx University, GDR University of Bucharest INCREST, Bucharest Politechnical Institute, Timi 90ara Politechnical Institute, Bucharest University of Cluj University of Cluj University of Timi90ara INCREST, Bucharest INCREST, Bucharest INCREST, Bucharest University of Timi 90ara University of Szeged, Hungary INCREST, Bucharest University of Bra90v Electrotimi 9 , Timi90ara INCREST, Bucharest Politechnical Institute, Timi 90ara University of Timi90ara Politechnical Institute, Bucharest University of Bucharest INCREST, Bucharest INCREST, Bucharest INCREST, Bucharest INCREST, Bucharest University of Indiana, USA Politechnical Institute, Timi90ara

11

PROGRAM OF THE CONFERENCE

MONDAY, June 2 SECTION A

Cha~~man: S.Teleman 16:30 - 17:00 R.N.GOLOGAN: Akcoglu's erg~dic theorem for some

nonpositive L -contractions. 17:10 - 17:40 C.APOSTOL; ~1.MARTIN: A C*-algebra approach to a

theorem of Cowen-Douglas. 17:50 - 18:20 R.MENNICKEN: Analytic perturbations of semi-Fred­

holm operators in locally convex spaces.

18:30 - 19:00 F.L.GILFEATHER:Nest subalgebras of von Neumann algebras.

SECTION B

Cha~~man: Gh. Bueu~

16:30 - 17:00 M.PELIGRAD: A tightness criterion for a class of random elements of D[O,I].

17:10 - 17:40 C.TUDOR: Solutions of stochastic integral equation&

TUESDAY, June 3 JOINT SESSION

Ch~~man: V.Vo~eule~eu

9:30 - 10:15 L.FIALKOW: Generalized derivations. 10:30 - 11:15 D.A.HERRERO: Quasidiagonality, similarity and ap­

proximation by nilpotent operators. 11:30 - 12:15 R.G.DOUGLAS: On the smoothness of elements of Ext.

SECTION A

Cha~~man: P.F~llmo~e

16:30 - 17:00 M.PIMSNER: Imbedding the irrational rotation C*­-algebra into an AF-algebra.

17:10 - 17~40 D.VOICULESCU: Remarks on Hilbert-Schmidt perturba­tions of almost normal operators.

17:50 - 18:20 S.POPA: Remarks on the Calkin algebra for certain singular extensions.

18:30 - 19:00 D.PETZ: On some subsets of von Neumann algebras.

PROGRAM OF THE CONFERENCE 13

SECTION B

Cha~~man: I.S~nge~

16:30 - 17:00 ?BALINTi A.STEPAN: Sur un systeme d'equations di­ferentielles intervenant dans un processus de separation.

17:10 - 17:40 E.DEUTSCH: Nested bounds for the Perron root of a nonnegative irreducible matrix.

17:50 - 18:20 F.POTRA: Error analysis for a class of Newton-like methods.

WEDNESDAY, June 4 JOINT SESSION

Cha~~man: R.G.Vougta~

9:30 - 10:15 r.SUCIU: Hodelling by L2-bounded analytic functions. 10:30 - 11:15 B.SZOKEFALVI-NAGY: The functional model of t con-

~ traction and the space L • 11:30 - 12:15 N.K.NIKOLSKII: Deux applications des operateurs de

Hankel.

SECTION A

Cha~~man: N.K.N~kot~k~~

16:30 - 17:00 B.NAGY: The spectral residuum of closed operators. 17:10 - 17:40 N.SUCIUi I.VALU9ESCU: The maximal function of

doubly commuting contractions. 17:50 - 18:20 L.KgRCHY: p-weak contractions. 18:30 - 19:00 E.DURSZT: Some connections between contractions

and power-bounded operators.

SECTION B Cha~~man: B.Fugtede

16:30 - 17:00 E.POPA: Morphisms of H-cones. 17:10 - 17:40 N.BOBOCi G.BUCUR: Strong Ray semi groups and stan­

dard H-cones. 17:50 - 18:20 L.STOICA: Feller resolvents.

THURSDAY, June 5 JOINT SESSION

Cha~~man: B.Szoke6atv~-Nagy

9:30 - 10:15 V.GEORGESCU: Algebraic scattering theory. 10:30 - 11:15 B.CHEVREAU: On M-spectral sets and rattionally-in­

variant subspaces. 11:30 - 12:15 C.APOSTOL: The spectral flavour of Scott Brown's

technique.

PROGRAM OF THE CONFERENCE 14

SECTION A Cha~~man: V.A.He~~e~o

16:30 - 17:00 R.F.OLIN: Algebras of subnormal operators. 17:10 - 17:40 I.CIORANESCU: On distribution-semigroups of subnor­

mal operators. 17:50 - 18:20 D.TIMOTIN: On Scott Brown's theorem. 18:30 - 19:00 N.PAVEL: Invariant subcones of a linear operator.

SECTION B

Cha~~man: M.Regh~i

16:30 - 17:00 T.GRZYBOWSKI: General procedure for distorted pattern reconstitution.

17:10 - 17:40 E.CAMpu: Multi-application associees aux multiequa­tions differentielles a retardement.

17:50 - 18:20 V.TROIE: Characteristic numbers for solutions of linear differential equations at a singu­lar pOint.

18:30 - 19:00 G.MIEL: Analysis of equations with smooth coeffi­cients.

SATURDAY, June 7 JOINT,SESSION

Cha~~man: J.P.W~!!~am~

9:30 - 10:15 S.TEL~1AN: Apnlications of Choquet theory to reduc­tion theory.

10:30 - 11:15 J.ANDERSON: Irreducible representations of B(H). 11:30 - 12:15 P.FILLMORE: Kasparov's stability theorem.

MONDAY, June 9 JOINT SESSION

Cha~~man: N.Boboe 9:30 - 10:15 V.JONES: Invariants for group actions on algebras.

10:30 - 11:15 A.OCNEANU: Actions of amenable groups on von Neu­mann algebras.

11:30 - 12:15 B.FUGLEDE: The fine topology in potential theory.

SECTION A

Cha~~man: V.Ga~pa~

16:30 - 17:00 P.I,A'TRUTA: On the continuity of averaqing tyoe onerators on some function spaces.

17:10 - 17:40 G.I,ODINI: On certain classes of normed vector spaces.

17:50 - 18:20 N.POPA: Complemented sublattices in Lorenz sequen­ce spaces without local-convexity.

18:30 - 19:00 D.VUZA: A theorem of Hahn-Banach type for modules over ordered rings.

PROGRAM OF THE CONFERENCE 15

TUESDAY, June 10 JOINT SESSION

Cha~4man: C.Apo4tol 9:30 - 10:15 N.BOBOC; G.BUCUR: Potentials on standard H-cones.

10:30 - 11:15 T.ANDO: Generators of positivity preserving semi­groups.

11:30 - 12:15 F.H.VASILESCU: Anticommuting selfadjoint operators.

SECTION A

Cha~4man: T.Ando 16:30 - 17:00 G.ECKSTEIN: Exact controllability and spectrum

assignement. 17:10 17:40 GR.ARSENEi Z.CEAU~ESCU: A functional model for in­

tertwining dilations. 17:50 - 18:20 C.PELIGRAD: Derivations of C*-crossed products. 18:30 - 19:00 N.K.NIKOLSII: Les sous-espaces invariantes et une

notion de capacite.

SECTION B

Cha~4man: V.V.Staneu 16:30 - 17:00 O.STANASILAi D.STANO~1IR: On certain non-linear sys­

tems. 17:10 - 17:40 G.MINEA: First integrals for the Euler equation of

incompressible fluids. 17:50 - 18:20 O.BERECHET: Parabolic equations with unbounded coef­

ficients.

WEDNESDAY, June 11 JOINT SESSION

Cha~4man: F.H.Va4~le4eu

9:30 - 10:15 K.SCHMtlDGEN: On perturbation of spectra of diagonal operators.

10:30 - 11:15 J.P.WILLIAMS: The range of a derivations: Open pro­blems.

11:30 - 12:15 E.ALBRECHT: On closed operator algebras generated by analytic functiGnal calculi.

SECTION A

Cha~4man: J.Ande44on 16:30 - 17:00 M.PUTINAR: Functional calculus with sections of an

analytic space. 17:10 - 17:40 G.DINESCU: Some results concerning semi-scalar

operators. 17:50 - 18:20 T.CONSTANTINESCUi A.GHEONDEA: Algebraic aspects of

the meromorphic functional calculus. 18:30 - 19:00 C.GROSU: Spectra of selfadjoint tenser product

operators and related applications.

PROGRAM OF THE CONFERENCE

THURSDAY, June 12 SECTION B

Cha~~man: I.Sue~u

9:30 - 10:00 I.A.RUS: Fixed point theorems for the sum of two mans.

16

10:10 - 10:40 D.O.RUS: Approximation properties of some classes of linear positive operators of spline type.

10:50 - 11:20 V.HIRI9i r1.MEGAN: Asymptotic behaviour for linear svstems with control.

11:30 - 12:00 P.TOPUZU: On the characteristic function and posi­tive systems in Hilbert spaces.