OT28: Operator Theory: Advances and Applications Vol. 28

Editor: I. Gobberg Tel Aviv University Ramat Aviv, Israel

Editorial Office: School of Mathematical Sciences Tel Aviv University RamatAviv, Israel

Editorial Board:

A. Atzmon (TelAviv) J. A: Ball (Blacksburg) L. de Branges (West Lafayette) K. Clancey (Athens, USA) L. A. Coburn (Buffalo) R. G. Douglas (Stony Brook) H. Dym (Rehovot) A. Dynin (Columbus) P. A. Fillmore (Halifax) C. Foias (Bloomington) . P. A. Fuhrmann (Beer Sheva) S. Goldberg (College Park) B. Gramsch (Mainz) J. A. Helton (La Jolla) D. Herrero (Tempe)

Honorary and Advisory Editorial Board:

P. R. Halmos (Santa Clara) T. Kato (Berkeley) P. D. Lax (New York) M. S. Livsic (Beer Sheva)

Birkhauser Verlag Basel· Boston· Berlin

M. A. Kaashoek (Amsterdam) T. Kailath (Stanford) H. G. Kaper (Argonne) S. T. Kuroda (Tokyo) P. Lancaster (Calgary) L. E. Lerer (Haifa) E. Meister (Darmstadt) B. Mityagin (Columbus) J. D. Pincus (Stony Brook) M. Rosenblum ( Charlottesville) J. Rovnyak (Charlottesville) D. E. Sarason (Berkeley) H. Widom (Santa Cruz) D. Xia (Nashville)

S. G. Mikhlin (Leningrad) R. Phillips (Stanford) B. Sz.-Nagy (Szeged)

Special Classes of Linear Operators and Other lbpics

1988

11th International Conference on Operator Theory Bucharest (Romania) June 2 -12, 1986

Volume Editors H. Helson C. M. Pearcy F.-H. Vasilescu D. Voiculescu

Managing Editor Gr. Arsene

Birkhauser Verlag Basel· Boston· Berlin

Volume Editorial Office:

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

CIP-Titelaufnahme der Deutschen Bibliothek

Special classes of linear operators and other topics /11 th Internat. Conference on Operator Theory, Bucharest (Romania), June 2 - June 12, 1986. Vol. ed. H. Helson ... Managing ed. Gr. Arsene. - Basel ; Boston ; Berlin : Birkhiiuser, 1988

(Operator theory ; Vol. 28) ISBN-13: 978-3-7643-1970-0

NE: Helson, Henry [Hrsg.]; International Conference on Operator Theory <11, 1986" Bucure~ti>; GT

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use a fee is payable to >,verwertungsgesellschaft Wort«, Munich.

© 1988 BirkhiiuserVerJag Basel

Softcover reprint of the hardcover 1 st edition 1988

ISBN-13: 978-3-7643-1970-0 e-ISBN-13: 978-3-0348-9164-6 001: 10.1007/978-3-0348-9164-6

BOROGOVAC,M.;LANGER,H.

'lJRUINSMA, P. ; DIJKSMA, A. ; de SNOO, H.

CHEVREAU,B.;PEARCY,C.

DOUGLAS, R.G.

DURSZT, E.

FORSTER, K.-H. ; NAGY, B.

GANCHEV, A. ; GREENBERG, W. ; van der MEE, C. V.M.

GOLDSTEIN, 1\1.5. ; GRABARNIC, G.Ya.

HELSON, H. ; MERRILL, K.D.

HERRERO, D.A.

JANZ, R.

KERCHY, L.

MASANI, P.R.

CONTENTS

Foreword .......................................... 7

List of participants •..........•.••..•....•.•.•. 8

Programme of the conference ••••..•...... 11

A characterization -of generalized zeros of negative type of matrix functions of the class Nn x n ••••.•......•... 17

K

Unitary dilations of contractions in IlK -spaces ......... .•.........•.. ............... 27

On Sheung's theorem in the theory of dual operator algebras ........•....•...•.. 43

On Silov resolution of Hilbert modules ••.........••...••..•...................•..• 51

On defect functions of contractions •..• 61

On the local spectral theory of positive operators .............................. 71

Perturbation analysis of analytic bisemigroups and applications to linear transport theory....................... 83

Almost sure convergence theorems in von Neumann algebras .................... 101

Cocycles on the circle. 11 ...••........••••••• 121

An essay on quasitriangularity .•...•...••. 125

Holomorphic families of subspaces of a Banach space .....•................•...•..• 155

On a conjecture of Teodorescu and Vasyunin ..................................... 169

On conditional homomorphisms and semi-norms on Banach groups and the unification of operator theory and measure theory ............................ 173

McINTOSH, A. ; PRYDE, A. ; RICKER, W.

NEUMANN, M.M.

PACKER, J.A.

PETERS, J.

PUTINAR, M.

SALINAS, N.

SUCIU, I.

WOLLENBERG, M.

ZAJAC, M.

Estimates for solutions of the operator m

equation L A.QB. = U •.•..•••......•..•.••.. 197 j=l J J

Decomposable operators and generalized intertwining linear transformations ••....•••••.•••••••••••.......... 209

Flow equivalence for dynamical systems and the corresponding C* -algebras •.••••...••.....•••••.•••••..•.••••..• 223

Connections between topological dynamics and oper.Q.tor algebras ....•.•.•. 243

Extreme hyponormal operators ••••••.•••. 249

The Grassmann manifold of a C*-algebra, and hermitian holomorphic bundles •••••.••.••.•••.•.••.•....• 267

Operatorial extrapolations and prediction ...•••••••••...............•.••••.. 291

On smooth asymptotic constants for the Poincare group. II •••••••....•.•..... 303

Hyperinvariant subspaces of weak contractions. II ..••••••••••.•....••••.•••.••••••• 317

7

FOREWORD

The Operator Theory conferences, organized by the Department of

Mathematics of INCREST and the University of Timi~oara, are conceived as a means to

promote cooperation and exchange of information between specialists in all areas of

operator theory. This volume consists of a careful selec£ion of papers contributed by

the participants of the 1986 Conference. They reflect most of the topics dealt with by

the modern operator theory, including recent advances in dual operator algebras and the

fnvariant subspace problem, operators in indefinite metric spaces, hyponormal,

quasi triangular and decomposable operators, various problems in C*- and W*-algebras

and so on.

The research contracts of the Department of Mathematics of INCREST with

the National Council for Science and Technology of Romania provided the means for

developing the research activity in mathematics; they represent the generous

framework of these meetings, too.

It is our pleasure to acknowledge the financial support of UNESCO which also

contributed to the success of this meeting.

We are indebted to Professor Israel Gohberg for including these Proceedings in

the OT Series and for valuable advice in the editing process. Birkhiiuser Verlag was very

cooperative in publishing this volume.

Camelia Minculescu, Iren Nemethi and Rodica Stoenescu dealt with the dif­

ficult task of typing the whOle manuscript using a Rank Xerox 860 word processor; we

thank them for the excellent job they did.

Organizing Committee,

Head of Mathematics Department of INCREST,

Zoia Ceausescu ,

Organizers,

F.-H. Vasilescu

Dan Voiculescu

8

ANGHEL, V. ARSENE, Grigore BACALU, Ion BAKONYI, Mihai BART, Harm BERECHET, Adriana BEZNEA, Lueian BOBOC, Nieu BOCA, Florin BRENNER, Valery V. BUCUR, Gheorghe 'CARTIANU, Dan CE.AU~ESCU, Zoia CEAU~U, Traian CHEVREAU, Bernard COLOJOARA, Ion CONSTANTINESCU, Tiberiu CORNEA, Emil DADARLAT, Marius DEACONU, Valentin DURSZT, Endre ESTERLE, Jean FORSTER, Karl-Heinz FURMANN, Paul A. GADIDOV, Radu GA~PAR, Dumitru GAVRUrA,p. GEORGESCU, Vladimir GHEONDEA, Aurelian GODINI, Glieeria GOLOGAN, Radu GRECEA, Valentin GROSU, Corina HALANA Y, Andrei HELSON, Henry HERTEA, I. HIR~, Viorel HORAK, Karel IFTIMIE, Viorel IONA~CU, lleana IORDANESCU, Radu IOSIFESCU, Marius

'IVANOV, A. JANSON, Svante

LIST OF PARTICIPANTS *)

Pitellti INCREST, Bucharest Poly technical Institute of Bucharest INCREST, Bucharest Erasmus Universiteit, Rotterdam, The Netherlands Statistical Centre, Bucharest INC REST, Bucharest Faculty of Mathematics, Bucharest Faculty of Mathematics, Bucharest Poly technical Institute of Tula, USSR INCREST, Bucharest ICECHIM, Bucharest INCREST, Bucharest Poly technical Institute of Timi~oara Universite de Bordeaux, France Faculty of Mathematics, Bucharest INCREST, Bucharest INCREST, Bucharest INC REST, Bucharest INCREST, Bucharest University of Szeged, Hungary Universite de Bordeaux, France Technische Universitat, West Berlin Ben-Gurion University, Beer Sheva, Israel INCREST, Bucharest University of Timilloara University of Timi~oara IFIN, Bucharest INC REST, Bucharest INCREST, Bucharest INCREST, Bucharest INCREST, Bucharest CIMIC, Bucharest Poly technical Institute of Bucharest University of California, Berkeley, USA ICECHIM, Bucharest University of Timisoara Mathematical Institute, Prague, Czechoslovakia University of Bucharest INCREST, Bucharest 1FT AR, Bucharest Statistical Centre, Bucharest ICECHIM, Bucharest Uppsala University, Sweden

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

JANZ, Raimund JOrrA, Maria JONAS, Peter Kf:RCHY,L8szIo MARTIN, Mircea MASANI, Pesi R. MATACHE, Valentin MATI'ER, Urs MIHALACHE, George MIHALACHE, Georgeta MISDOLEA, A. MULLER, Vladimir NAGY, Bela NAGY, Gabriel NENCIU, George NICA, Alexandru NICULESCU, Constantin NIECHWIEJ, Jan NISTOR, Victor

'1(UTIcA, Viorel P~CHKE, William L. PASNICU, Comel PAUNESCU, Doru PEARCY, Carl M. PETERS, Justin PETRESCU, Steliana PIMSNER, Mihai POPA, Nicolae POPA, Sorin POPESCU, Gelu POPESCU, Gheorghe PRUNARU,Bebe PTAK, Vlastimil PURCARU, C. PUTINAR, Mihai RADULESCU, Florin REGH~, Mircea RICKER, Wemer J. RUDOL, Krzysztof SALINAS, Norberto Sl.OCINSKI, Marek STRA TIL!, Seman SUCIU, Ion' SUCIU, Nicolae TALP~, Florin TERE~ENCO, Alexandru TIMOTIN, Dan TODOROV, Todor TOPUZU, Paul TOROK, Andrei VALU~ESCU, Hie van der MEE, Cornelis V ASILESCU, Florian-Horia VOICULESCU, Dan

University of Konstanz, West Germany INCREST, Bucharest Mathematical Institute, Berlin, GDR University of Szeged, Hungary INCREST, Bucharest University of Pittsburgh, USA University of Timi~oara University of Zilrich, Switzerland 1FT AR, Bucharest INC REST, Bucharest ICECHIM, Bucharest Mathematical Institute, Prague, Czechoslovakia Technical University, Budapest, Hungary INCREST, Bucharest IFIN, Bucharest Faculty of Mathematics'; Bucharest University of Craiova Institute of Mathematics, Krakow, Poland Faculty of Mathematics, Bucharest Faculty of Mathematics, Bucharest University of Kansas, USA INCREST, Bucharest Poly technical Institute of Timi~oara University of Michigan, USA Iowa State University, Carver Hill, USA INCREST, Bucharest INCREST, Bucharest INCREST, Bucharest INCREST, Bucharest INCREST, Bucharest ITCI, Bucharest INCREST, Bucharest Mathematical Institute, Prague, Czechoslovakia Craiova INC REST, Bucharest INC REST, Bucharest University of Timi~oara Macquarie University, North Ryde, Australia Institute of Mathematics, Krakow, Poland University of Kansas, USA Jagiellonian University, Poland INC REST, Bucharest INCREST, Bucharest University of Timi~oara ITCI, Bucharest University of Timi~oara INCREST, Bucharest Institute of Mathematics, Sofia, Bulgaria University of Timi~oara University of Timi~oara INCREST, Bucharest Clarkson University, Postdam, USA INCREST, Bucharest INCREST, Bucharest

9

10

VOLANSCHI, C. VUZA, Dan WENZL, Hans WOLLENBERG,Marur~ ZAJAC, Miehal ZHANG, Haitao ZORILESCU, Dan

Centre of Chemical Physics, Bucharest INCREST, Bucharest Columbia University, USA Mathematical Institute, Berlin, GDR MUSA V, Bratislava, Czechoslovakia Faculty of Mathematics, Bucharest IGC, Bucharest

PROGRAMME OF THE CONFERENCE

Tuesday, June 3

Chairman: F.-H. Vasilescu

C.M.Pearcy: Some remarks on the classes A, Al and A~o .

I.Suciu: Operatorial extrapolation and prediction.

P.R.Masani: Conditional additivity on Banach groups.

11

9.30-10.15

10.25-11.10

11.20-12.05

12.15-12.45 T.Constantineseu; A.Gheondea: Unitary dilations and their characteristic functions in Krein spaces.

Chairman: D.Ga~par

16.00-16.30 P.Jonas: On the trace formula of perturbation theory for definitizable operators in Krein spaces.

16.35-17.05 L.Kerchy: Invariant subspaces of C10-contractions.

17.10-17.25 P.Gavruta: On intertwining extensions.

Wednesday, June 4

Chairman: C.M.Pearcy

9.30-10.15 P.A.Fuhrmann: Block Hankel matrix inversion.

10.25-11.10 H.Bart: Wiener-Hopf equations with symbols analytic in a strip.

11.20-11.50 Gr.Arsene; Zoia Cea~eseu; T.Constantineseu: Multiplicative properties in the structure of contractions.

11.55-12.25 T.Constantineseu: A maximum entropy analysis for contractive inter­twining dilations.

12.30-13.00 D.Timotin: On the geometry of certain functional models for contrac­tions.

Seminar

14.00-15.05 J.Cuntz: Topological Markov chains and C*-algebras.

Chairman: I.Suciu

16.00-16.30 D.Gawar; N.Suciu; I.VaIu!!lescu: Maximal functions and semispectral measures on T2.

12

16.35-16.50

16.55-17.10

17.15-17.30

17.35-17.50

17.55-18.10

E.Durszt: On defect functions of contractions.

G.Popescu: Models for sequences of contractions.

B.Prunaru: Sufficient conditions for membership in the classes A and Ay.,o'

M.SIoeinski: Models of commuting contractions and isometries.

V.Ptak: Intertwining relations for Hankel matrices.

Thursday, June 5

Chairman: P.A.Fuhrmann

9.30-10.15 V.Georgescu: Asymptotic estimates for solutions of differential· equations with operator-valued coefficients.

10.25-11.10 H.Helson: A group of theorems in ergodic theory.

11,.20-12.05 F.-H.Vasilescu: Spectral theory in quotient Frechet spaces.

12.15-13.00 8.Chevreau: Pettis lemma and topological properties of dual algebras.

14.45-15.55

14.15-15.45

Seminar

P.A.Fuhrmann: Riccati equations.

H.Wenzl: Knots and subfactors.

Chairman: V.Ptak

16.00-16.30 M.Putinar: On extremal hyponormal operators.

16.35-17.05 K.Rudol: Spectra of orthogonal sums of subnormal pairs.

17.10-17.25 M.Reghi~; P.Topuzu: On some applications of Schauder decomposable operators.

17.30-17.45 Zhang Haitao: Fredholm theory for morphisms in quotient Banach spaces.

17.50-18.05 J.Nieehwiej: Some problems concerning the joint spectral measures of unbounded operators.

Friday, June 6

Chairman: P.R.Masani

9.30-10.15 N.Popa: Topological vector space properties of vector-valued Hardy spaces.

10.25-11.10 G.Nenciu: Operator theory aspects of singular perturbations in quantum mechanics.

11.20-11.50 M.Wollenberg: Smooth asymptotic constants for the Poincare group.

13

12.00-12.30 M.Martin: Analytic functions into a Grassman manifold and the Cowen­- Douglas class.

Seminar

14.00-15.40 J.Cuntz: Simplicial C* -algebras.

Chairman: H.Bart

15.55-16.10 P.Gavru~a: On generalized Hausdorff operators.

16.15-16.30 T.S.Todorov: On commutativity of symmetric operators.

16.35-16.50 A.Ter~enco: Quotient Banach spaces and in~erpolation theory.

16.55-17.10 C.Volanschi: Polynomial complexity for the isomorphism problem of operator algebras.

Monday, June 9

Chairman: J.Cuntz

9.30-10.15 M.losifescu: A class of operators with applications to piecewise mono­tonic transformations.

10.25-11.10 D.Voiculescu: Multiplication of certain non-commuting random variables.

11.20-12.05 N.Salinas: A natural connection on the Grassmann manifold of a C * -algebra.

12.15-13.00 M.Pimsner: KK-groups of crossed products by groups acting on trees.

Seminar

14.15-15.45 H.Wenzl: Knots and subfactors.

Chairman: W.Paschke

16.00-16.45 J.Esterle: Banach algebras with approximate identities close to their ex>

square and representations of H .

16.55-17.25 V.Nistor: Stable range of tensor products of extensions of K by C(X).

17.30-17.45 C.Pasnicu: On inductive limits of certain C*-algebras of the form C(X)~F.

17.50-18.20 M.Dildilrlat: Inductive limits of C*-algebras related to a tower of coverings.

14

Tuesday, June 10

Chairman: N.Salinas

9.30-10.15 W_.Pasehke: K-theory for discrete group C* -algebras from combinatorial information.

10.25-11.10 J.Cuntz: A new look at KK-theory.

11.20-12.05 H.Wenzl: Subfactors and Hecke algebras.

12.15-13.00 S.Popa: On Connes' correspondences.

Seminar

14.15-15.45 S.Janson: Hankel forms on Hilbert spaces of f~nctions of several complex variables. .

Chairman: $.Strcitilci

16.0Q-16.30 J.Paeker: Flow equivalence for homeomorphisms and the corresponding C * -algebra.

16.35-17.05 J.Peters: The ideal structure of certain nonselfadjoint operator algebras.

17.10-17.25 V.V.Brenner: Spectral properties of random difference operators and functional equations.

17.50-18.05 U.Matter: A generalization of the Pietsch factorization theorem.

18.10-18.25 C.Nieulescu: The centralizer associated to an Alfsen-Effros type order relation.

Wednesday, June 11

Chairman: H.Helson

9.30-10.15

10.25-11.10

11.20-12.05

12.15-12.45

N.Boboe; Gh.Bucur: Perturbations in Dirichlet spaces.

S.Janson: Paracommutators - Boundedness and Schatten-von Neumann properties.

V.lftimie: Sur la completitude asymptotique dans Ie cas "long-range".

F.Radulescu; F.-H.Vasilescu: Matrix operators and hyperinvariant sub­spaces.

Seminar

14.15-15.45 J.Cuntz: What is KK?

14.30-15.45 H.Bart: Minimal factorization, stable invariant subspaces and indefinite metrics.

Chairman: I.Colojoara

16.00-16.30 D.Vuza: The components of a positive operator.

16.35-16.50 V.Muller: On quasialgebraic operators.

15

16.55-17.10 M.Dad8rlat; V.Deaconu: On some homeomorphisms of>:C(X)®F r""C(Y):&)F 2 with F. finite dimensional.

I

17.15-17.30 M.Zajac: When Hyplat(T) is determined by the bicommutant of T?

17.35-17.50 K.-H.Forster: Local spectral theory of positive operators.

17.55-18.10 R.Janz: Holomorphic families of subspaces of a Banach space.

18.15-18.30 C.van der Mee: Perturbation analysis of analytic bisemigroups.

Thursday, June 12

Chairman: M.Reghi~

10.00-10.45

10.50-11.20

11.25-11.55

12.00-12.30

D.Vuza: Strongly latticial classes of operators and their connection with the theory of principal modules.

V.Ptalq P.Vrbova: An abstract model for compressions.

B.Nagy: On the spectral singularities of the truncated shift.

W.J.Ricker: The solution of systems of operator equations in Banach spaces.