Recent Advances in Operator Theory and Related Topics: The Béla Szökefalvi-Nagy Memorial Volume

705 Pages·2001·17.963 MB·English

by  Daniel Alpay, Israel Gohberg (auth.), László Kérchy, Prof. I. Gohberg, Ciprian I. Foias, Prof. H. Langer (eds.)

Operator Theory: Advances and
Applications
VoI. 127
Editor:
1. Gohberg
Editorial Board:
J. Arazy (Haifa) L.E. Lerer (Haifa)
A. Atzmon (Tel Aviv) E. Meister (Darmstadt)
J. A. BaII (Blacksburg) B. Mityagin (Columbus)
A. Ben-Artzi (Tel Aviv) V. V. Peller (Manhattan, Kansas)
H. Bercovici (Bloomington) J. D. Pincus (Stony Brook)
A. B6ttcher (Chemnitz) M. Rosenblum (Charlottesville)
K. Clancey (Athens, USA) J. Rovnyak (Charlottesville)
L. A. Coburn (Buffalo) D. E. Sarason (Berkeley)
K. R. Davidson (Waterloo, Ontario) H. Upmeier (Marburg)
R. G. Douglas (Stony Brook) S. M. Verduyn-Lunel (Amsterdam)
H. Dym (Rehovot) D. Voiculescu (Berkeley)
A. Dynin (Columbus) H. Widom (Santa Cruz)
P. A. Fillmore (Halifax) D. Xia (Nashville)
P. A. Fuhrmann (Beer Sheva) D. Yafaev (Ren nes)
S. Goldberg (College Park)
B. Gramsch (Mainz) Honorary and Advisory
G. Heinig (Chemnitz) Editorial Board:
J. A. Helton (La Jolla) C. Foias (Bloomington)
M.A. Kaashoek (Amsterdam) P. R. Halmos (Santa Clara)
H.G. Kaper (Argonne) T. Kailath (Stanford)
S.T. Kuroda (Tokyo) P. D. Lax (New York)
P. Lancaster (Calgary) M. S. Livsic (Beer Sheva)
Recent Advancesin
Operator Theory
and Related Topics
The Bela Szokefalvi-Nagy Memorial Volume
Laszl6 Kerchy
Ciprian Foias
Israel Gohberg
Heinz Langer
Editors
Springer Basel AG
Editors:
Laszl6 Kerchy Prof. 1. Gohberg
Bolyai Institute School of Mathematical Sciences
University of Szeged Raymond and Beverly Sackler
Aradi Vertanutik Tere l Faculty of Exact Sciences
6720 Szeged Tel Aviv University
Hungary Ramat Aviv 69978
Israel
Ciprian 1. Foias
Department of Mathematics Prof. H. Langer
Indiana University Mathematik
Bloomington, IN 47405-4301 Technische Universităt Wien
USA Wiedner Hauptstrasse 8-10/1411
1040Wien
Austria
2000 Mathematics Subject Classification 47-06
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA
Deutsche Bibliothek Cataloging-in-Publication Data
Recent advances in operatory theory and related topics : the Bela Szokefalvi-Nagy
memorial volume / Lâszlo Kerchy ... ed. . -Basel ; Boston; Berlin: Birkhăuser, 2001
(Operator theory ; VoI. 127)
ISBN 3-7643-6607-9
ISBN 978-3-0348-9539-2 ISBN 978-3-0348-8374-0 (eBook)
DOI 10.1007/978-3-0348-8374-0
This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concemed,
specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms
or in other ways, and storage in data banks. For any kind of use pennission of the copyright owner must be obtained.
© Springer Basel AG 2001
Originally published by Birkhăuser Verlag 2001
Member of the BertelsmannSpringer Publishing Group
Printed on acid-free paper produced from chlorine-free pulp. TCF ce
Cover design: Heinz Hiltbrunner, Basel
ISBN 3-7643-6607-9
www.birkhăuser-science.com
987654321
Contents
Preface .................................................................. vii
Portrait of Bela Szokefalvi-Nagy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
C. FOIAS, Farewell speech................................................. xi
I. GOHBERG, Reminiscences of Bela Szokefalvi-Nagy ....................... Xlll
Photographs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
L. KERCHY and H. LANGER, Bela Szokefalvi-Nagy 1913-1998 ................ xxi
Publications of Bela Szokefalvi-Nagy ..................................... xxxix
D. ALPAY and I. GOHBERG, Inverse problems associated to a canonical differ-
ential system ........................................................... 1
T. ANDO, Construction of Schwarz norms ................................. 29
Yu. M. ARLINsKII, S. HASSI, Z. SEBESTYEN and H. S. V. DE SNOO, On the class
of extremal extensions of a nonnegative operator ........................ 41
Z. D. AROVA, On Livsic-Brodskii nodes with strongly regular J-inner char-
acteristic matrix functions in the Hardy class ........................... 83
B. BAGCHI and G. MISRA, Scalar perturbations of the Sz.-Nagy-Foias charac-
teristic function ........................................................ 97
H. BERCOVICI and W. S. LI, Inequalities for eigenvalues of sums in a von Neu-
mann algebra .......................................................... 113
A. BISWAS, C. FOIAS and A. E. FRAZHO, Weighted variants of the Three Chains
Completion Theorem ................................................... 127
G. CASSIER, Semigroups in finite von Neumann algebras................... 145
J. B. CONWAY and G. PRAJITURA, Singly generated algebras containing a com-
pact operator .......................................................... 163
C. D'ANTONI and L. Zsroo, Analytic extension of vector valued functions... 171
R. G. DOUGLAS and G. MISRA, On quotient modules........................ 203
J. ESCHMEIER, On the structure of spherical contractions. . . . . . . . . . . . . . . . . . . 211
J. ESTERLE, Apostol's bilateral weighted shifts are hyper-reflexive. . . . . . . . . . 243
M. FUJII and Y. SE~, Wielandt type extensions of the Heinz-Kato--Furuta
inequality .............................................................. 267
T. FURUTA, Logarithmic order and dual logarithmic order................. 279
D. GA§PAR and N. Sucru, On the generalized von Neumann inequality...... 291
L. GE and D. HADWIN, Ultraproducts of C*-algebras ....................... 305
vi Contents
C. Gu and R. I. TEODORESCU, Intertwining extensions and a two-sided corona
problem ................................................................ 327
G. HOFMANN, On self-polar Hilbertian norms on (indefinite) inner product
spaces.................................................................. 349
J. A. HOLBROOK, Schur norms and the multivariate von Neumann inequality 375
J. JANAS and S. NABOKO, Spectral properties of selfadjoint Jacobi matrices
coming from birth and death processes ................................. 387
L. KERCHY, On the hyperinvariant subspace problem for asymptotically non-
vanishing contractions .................................................. 399
A. M. KRAGELOH and B. S. PAVLOV, Unstable dynamics on a Markov back-
ground and stability in average ......................................... 423
H. LANGER, H. S. V. DE SNOO and V. A. YAVRIAN, A relation for the spectral
shift function of two self-adjoint extensions ............................. 437
B. LE GAC and F. MORICZ, Beppo Levi and Lebesgue type theorems for bundle
convergence in noncommutative L -spaces .............................. 447
2
L. MOLNAR, *-semigroup endomorphisms of B(H) ......................... 465
S. NABOKO and R. ROMANOV, Spectral singularities, Szokefalvi-Nagy-Foias
functional model and the spectral analysis of the Boltzmann operator ... 473
J. M. A. M. VAN NEERVEN, Uniqueness of invariant measures for the stochastic
Cauchy problem in Banach spaces ...................................... 491
M. PUTINAR and H. S. SHAPIRO, The Friedrichs operator of a planar domain.
II ...................................................................... 519
M. SABAC, Localization of the Wielandt-Wintner Theorem................ 553
P. G. SPAIN, Order and square roots in hermitian Banach *-algebras ....... 561
J. STOCHEL and F. H. SZAFRANIEC, Unitary dilation of several contractions .. 585
M. UCHIYAMA, Inequalities for semibounded operators and their applications
to log-hyponormal operators............................................ 599
F.-H. VASILESCU, Operator moment problems in unbounded sets........... 613
J. WERMER, The argument principle and boundaries of analytic varieties... 639
Conference Program...................................................... 661
List of Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667
Preface
Bela Szokefalvi-Nagy, one of the founders of modern operator theory, and one
of its major contributors, passed away on December 21, 1998. To honour him, a
Memorial Conference for Bela Sz6kefalvi-Nagy was held on August 2-6, 1999, in
Szeged, Hungary, in which 91 mathematicians from all over the world took part.
There were 19 plenary lectures in the morning and 63 talks in two parallel sessions
in the afternoon.
The present volume contains proceedings and other research papers of the con
ference participants, and also 6 articles of distinguished experts who were unable to
attend. These 35 articles present original recent results in various areas of operator
theory and connected fields, many of them strongly related to contributions of Bela
Sz.-Nagy. As usual, all the papers in this volume were refereed.
The camera ready copy of the volume, made by the Fyx Bt. (Szeged), was
financed by the Bolyai Institute of the University of Szeged and by the Hungarian
NFS Research Grant T 035123. Special thanks go to Erzsebet Szokefalvi-Nagy for
providing the photos from the family album.
viii
Bela Szokefalvi-Nagy, 1980
Farewell speech
CIPRIAN FOIAS
On August 3, 1999, at the grave site in Szeged
to the participants of the Memorial Conference
Dear Colleagues,
We have come here to bring our hommage to Bela Szokefalvi-Nagy, a man of
high distinction, an affectionate and effective parent and a great mathematician.
Although a direct descendent on the male line from a military man ennobled for
his valor in battles against the Turks, Bela did not grow up as the scion of an
opulent family. His family had to quit their town, where Bela was born, on a
matter of principle. They came to Szeged, where Bela's father, an accomplished
mathematician, found adoquate position. Still, Bela during his college years had to
privately tutor other students. Bela was a student of F. Riesz and A. Haar, but not
in the sense in which we understand it today, neither in the sense in which I was
Bela's de facto student in Operator Theory. In that time Bela had to bootstrap
himself up to eventually become one of F. Riesz's peers in the branch of mathemat
ics which is now Operator Theory. In fact, while still in his twenties, Bela wrote
the first monograph in pure Operator Theory. It was written in French, but when
van der Waerden received a copy of the manuscript he immediately accepted it for
publication in the prestigious "Ergebnisse" series, but in a German translation. Al
most all leading mathematicians in Bela's generation learned Spectral Theory from
Bela's short but dense monograph. The scientific collaboration between Riesz and
Sz.-Nagy effectively took off only after Bela has proven himself as an exceptional
mathematician. The culminating result of that collaboration was the Riesz-Sz.
Nagy book on Functional Analysis, one of the most read and qouted mathematical
treatises in the second half of this century. Among the other outstanding works of
Bela in that time let me mention the following two: First Bela's discovery that the
Banach generalized limit (which until then was only a mathematical curiosity) can
be made a nonconstructive but very effective tool in Operator Theory. A lot of
mathematics came out from that discovery. Bela had the magic wand that changed