Recent Advances in Operator Theory: The Israel Gohberg Anniversary Volume International Workshop in Groningen, June 1998

591 Pages·2001·19.41 MB·English

by  Vadim Adamyan

Operator Theory: Advances and
Applications
Vol.124
Editor:
I. Gohberg
Editorial Office:
School of Mathematical H.G. Kaper (Argonne)
Sciences ST. Kuroda (Tokyo)
Tel Aviv University P. Lancaster (Calgary)
Ramat Aviv, Israel L.E. Lerer (Haifa)
E. Meister (Darmstadt)
Editorial Board: B. Mityagin (Columbus)
J. Arazy (Haifa) V. V. Peller (Manhattan, Kansas)
A. Atzmon (Tel Aviv) J. D. Pincus (Stony Brook)
J. A. Ball (Blacksburg) M. Rosenblum (Charlottesville)
A. Ben-Artzi (Tel Aviv) J. Rovnyak (Charlottesville)
H. Bercovici (Bloomington) D. E. Sarason (Berkeley)
A. Böttcher (Chemnitz) H. Upmeier (Marburg)
K. Clancey (Athens, USA) S. M. Verduyn-Lunel (Amsterdam)
L. A. Coburn (Buffalo) D. Voiculescu (Berkeley)
K. R. Davidson (Waterloo, Ontario) H. Widom (Santa Cruz)
R. G. Douglas (Stony Brook) D. Xia (Nashville)
H. Dym (Rehovot) D. Yafaev (Rennes)
A. Dynin (Columbus)
P. A. Fillmore (Halifax) Honorary and Advisory
P. A. Fuhrmann (Beer Sheva) Editorial Board:
S. Goldberg (College Park) C. Foias (Bloomington)
B. Gramsch (Mainz) P. R. Haimos (Santa Clara)
G. Heinig (Chemnitz) T. Kailath (Stanford)
J. A. Helton (La Jolla) P. D. Lax (New York)
M.A. Kaashoek (Amsterdam) M. S. Livsic (Beer Sheva)
Recent Advances in
Operator Theory
The Israel Gohberg Anniversary Volume
International Workshop in Groningen, June 1998
A. Dijksma
MA Kaashoek
A.C.M. Ran
Editors
Springer Basel AG
Editors:
A. Dijksma M.A. Kaashoek
Department of Mathematics Division of Mathematics and Computer Science
University of Groningen Faculty of Sciences
P.O. Box 800 Vrije Universiteit
9700 AV Groningen De Boelelaan 1081a
The Netherlands 1081 HV Amsterdam
e-mail: [email protected] The Netherlands
e-mail: [email protected]
A.C.M. Ran
Division of Mathematics and Computer Science
Faculty of Sciences
Vrije Universiteit
De Boelelaan 1081a
1081 HV Amsterdam
The Netherlands
e-mail: [email protected]
2000 Mathematics Subject Classification 47-06; 46, 45, 30, 34, 35, 93
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 operator theory : the Israel Gohberg anniversary volume ;
international workshop in Groningen, June 1998 / A. Dijksma ... ed.. - Basel; Boston ;
Berlin: Birkhäuser, 2001
(Operator theory ; Vol. 124)
ISBN 978-3-0348-9516-3 ISBN 978-3-0348-8323-8 (eBook)
DOI 10.1007/978-3-0348-8323-8
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned,
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© 2001 Springer Basel AG
Originally published by Birkhäuser Verlag, Basel - Boston - Berlin in 2001
Softcover reprint of the hardcover 1st edition 2001
Printed on acid-free paper produced from chlorine-free pulp. TCF <*>
Cover design: Heinz Hiltbrunner, Basel
ISBN 978-3-0348-9516-3
98765432 1 www.birkhasuer-science.com
Israel Gohberg
Contents
Picture of Israel Gohberg ............................................... v
Editorial preface ...................................................... xi
Speeches given at the conference dinner in celebration
ofIsrael Gohberg's 70-th anniversary .................................. xiii
Curriculum vitae ofIsrael Gohberg ................................... xxiii
Rien Kaashoek
A review of the mathematical work of Israel Gohberg xxvii
List of publications of Israel Gohberg ................................ xxxiii
Vadim Adamyan, Reinhard Mennicken and Vjacheslav Pivovarchik
On the spectral theory of degenerate quadratic operator pencils . . . . . . . .. 1
Daniel Alpay, Vladimir Bolotnikov and Leiba Rodman
Two-sided tangential interpolation for Hilbert-Schmidt operator
functions on polydisks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21
D. Alpay, A. Dijksma and Y. Peretz
Nonstationary analogs of the Hergiotz representation theorem:
realizations centered at an arbitrary point ............................ 63
Yury Arlinskii
Characteristic functions of maximal sectorial operators . . . . . . . . . . . . . . .. 89
T.Ya. Azizov, A.I. Barsukov, A. Dijksma and P. Jonas
Similarity between Krein space bicontractions
and Hilbert space contractions ...................................... 109
Hari Bercovici and Thomas Smotzer
Classification of cyclic invariant subspaces of Jordan operators ....... 131
Paul Binding and Rostyslav Hryniv
Elliptic spectral problems of higher order with eigenparameter
dependent boundary conditions..................................... 145
viii Contents
V.B. Bogevolnov, A.B. Mikhallova, B.S. Pavlov and A.M. Yafyasov
About scattering on the ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 155
Ramon Bruzual and Marisela Dominguez
Dilation of generalized Toeplitz kernels on lexicographic r x R ....... 175
HarryDym
On Riccati equations and reproducing kernel spaces .. . . . . . . . . . . . . . . .. 189
Torsten Ehrhardt
A status report on the asymptotic behavior of Toeplitz
determinants with Fisher-Hartwig singularities ...................... 217
Volker Hardt and Reinhard Mennicken
On the spectrum of unbounded off-diagonal 2 x 2 operator
matrices in Banach spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 243
J. Janas and S. Naboko
Multithreshold spectral phase transitions for a class
of Jacobi matrices .................................................. 267
M.A. Kaashoek and H.J. Woerdeman
Positive extensions and diagonally connected patterns ................ 287
Eizaburo Kamei
Parametrized Furuta inequality and its applications .................. 307
I. Karelin L. Lerer and A.C.M. Ran
J -symmetric factorizations and algebraic Riccati equations. . . . . . . . . .. 319
A.G. Kostyuchenko and A.A. Shkalikov
Scattering of waves by periodic gratings and factorization problems .. 361
Heinz Langer, Alexander Markus and Christiane Tretter
Comer of numerical ranges ......................................... 385
M.M. Malamud
On some classes of extensions of sectorial operators
and dual pairs of contractions ....................................... 401
S.A.M. Marcantognini and M.D. Moran
Liftings of intertwining operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 451
Alexander Markus and Vladimir Matsaev
Some estimates for the resolvent and for the lengths
of Jordan chains of an analytic operator function . . . . . . . . . . . . . . . . . . . .. 473
Contents IX
David Ogle, Nicholas Young
The Parrott problem for singular values 481
B. de Pagter, F.A. Sukochev and H. Witvliet
Unconditional decompositions and Schur-type multipliers ............ 505
Vyacheslav Pivovarchik
Scattering in a loop-shaped waveguide ............................... 527
Steffen Roch
Pseudospectra of operator polynomials .............................. 545
Editorial Preface
This volume contains a selection of papers in modern operator theory and its
applications. Most of them are directly related to lectures presented at the Inter
national Workshop on Operator Theory and its Applications held at the University
of Groningen (IWOTA-98) in Groningen, the Netherlands, from June 30-July 3,
1998. The workshop was attended by 97 mathematicians-of which 12 were PhD
or postdoctoral students-from 19 countries. The program consisted of 19 plenary
lectures of 40 minutes and 72 lectures of 30 minutes in 4 parallell sessions.
The present volume reflects the wide range and rich variety of topics presented
and discussed at the workshop. The papers deal with operator polynomials and
analytic operator functions, with spectral problems of (partial) differential oper
ators and related operator matrices, with interpolation, completion and extension
problems, with commutant lifting and dilation, with Ricatti equations and real
ization problems, with scattering theory, with problems from harmonic analysis,
and with topics in the theory of reproducing kernel spaces and of spaces with an
indefinite metric. All papers underwent the usual refereeing process.
This volume is dedicated to Israel Gohberg, one of the initiators of the series of
IWOTA workshops and president for life of its steering committee, on the occasion
of his 70-th birthday. The workshop at Groningen, which is the tenth in the series,
turned out to be a particularly appropriate occasion for a pre-celebration. The
texts of the speeches delivered at the workshop diner, honoring Israel Gohberg
and reflecting on his outstanding achievements and wonderful personality, are
included in this volume. We have also added to this volume his CV and complete
list of publications (listing 21 books and 401 articles), and a short description of
his mathematical work.
The Editors.
Speeches Given at the Conference
Dinner in Celebration of
Israel Gohberg's 70-th Birthday
At the conference dinner a number of speeches were given, as a pre-celebration ofIsrael Gohberg's
70-th birthday later that year. The texts here below have been prepared by Harm Bart, Harry
Dym, Bill Helton, Heinz Langer, Alek Markus, Cora Sadosky, and Hugo Woerdeman. The order
of the texts corresponds to the way the speeches were presented at the dinner.
1 To You, Izea!, by Alek Markus
I have known Israel Gohberg most of my life - since 1951. And for most of my
life I have been proud of being his first disciple. I don't mean the best, but the first
I was.
In 1959 we began to work together, for almost 15 years he was my boss and a
very good boss, I have to say. Unfortunately I was not a very good subordinate, as
I understand now. Whenever he asked me to do something, I immediately asked
him if it was worth doing at all. He never lost patience with me and very soon
I realized that he was almost always right and I was nearly always wrong. He
realized that too, because he always told me: "You should never argue with me,
because I am old and wise." He did seem old to me then - he was already 31 in
1959. But about 10 years before the time described, Israel was not quite so old
and, I suspect, not quite so wise.
To illustrate the last point I would like to tell you a story. There were two char
acters in the story - one Israel Gohberg, the name of the other one will come
up later. The events in the story are connected with elections to the Soviet Parlia
ment. Those who lived in the former Soviet Union know that the Soviet
Parliament was nothing like a parliament and the elections were nothing like elec
tions. There was always one candidate for every vacant position and the result of
the election was always 99.99% "for".
On the morning of some election day Israel came to his polling station and took
a ballot paper with the name of the only candidate ... Joseph Stalin! In accor
dance with his previous firm decision Israel went into the booth, which itself was
a very unusual and risky action, and crossed out the hated name. He then carefully
folded the ballot paper and put the paper into the ballot box. Next morning he
opened the newspaper. He was eager to know how many people were as brave as
him. What he read was: ''The result of the voting for Joseph Vissarionovich Stalin