Advances in Structured Operator Theory and Related Areas: The Leonid Lerer Anniversary Volume

258 Pages·2013·2.89 MB·English

by  M. A. Kaashoek (auth.), Marinus A. Kaashoek, Leiba Rodman, Hugo J. Woerdeman (eds.)

Operator Theory
Advances and Applications
237
Marinus A. Kaashoek
Leiba Rodman
Hugo J. Woerdeman
Editors
Advances in
Structured
Operator Theory
and Related Areas
The Leonid Lerer Anniversary Volume
Operator Theory: Advances and Applications
Volume 237

Founded in 1979 by Israel Gohberg

Editors:
Joseph A. Ball (Blacksburg, VA, USA)
Harry Dym (Rehovot, Israel)
Marinus A. Kaashoek (Amsterdam, The Netherlands)
Heinz Langer (Vienna, Austria)
Christiane Tretter (Bern, Switzerland)

Associate Editors: Honorary and Advisory Editorial Board:
Vadim Adamyan (Odessa, Ukraine) Lewis A. Coburn (Buffalo, NY, USA)
Wolfgang Arendt (Ulm, Germany) Ciprian Foias (College Station, TX, USA)
Albrecht Böttcher (Chemnitz, Germany) J.William Helton (San Diego, CA, USA)
B. Malcolm Brown (Cardiff, UK) Thomas Kailath (Stanford, CA, USA)
Raul Curto (Iowa, IA, USA) Peter Lancaster (Calgary, Canada)
Fritz Gesztesy (Columbia, MO, USA) Peter D. Lax (New York, NY, USA)
Pavel Kurasov (Stockholm, Sweden) Donald Sarason (Berkeley, CA, USA)
Leonid E. Lerer (Haifa, Israel) Bernd Silbermann (Chemnitz, Germany)
Vern Paulsen (Houston, TX, USA) Harold Widom (Santa Cruz, CA, USA)
Mihai Putinar (Santa Barbara, CA, USA)
Leiba Rodman (Williamsburg, VA, USA)
Ilya M. Spitkovsky (Williamsburg, VA, USA)

Subseries
Linear Operators and Linear Systems
Subseries editors:
Daniel Alpay (Beer Sheva, Israel)
Birgit Jacob (Wuppertal, Germany)
André C.M. Ran (Amsterdam, The Netherlands)

Subseries
Advances in Partial Differential Equations
Subseries editors:
Bert-Wolfgang Schulze (Potsdam, Germany)
Michael Demuth (Clausthal, Germany)
Jerome A. Goldstein (Memphis, TN, USA)
Nobuyuki Tose (Yokohama, Japan)
Ingo Witt (Göttingen, Germany)
Marinus A. Kaashoek
Leiba Rodman
Hugo J. Woerdeman
Editors
Advances in
Structured Operator Theory
and Related Areas
The Leonid Lerer Anniversary Volume
Editors
Marinus A. Kaashoek Leiba Rodman
Department of Mathematics, FEW Department of Mathematics
VU University College of William and Mary
Amsterdam Williamsburg
Netherlands USA
Hugo J. Woerdeman
Department of Mathematics
Drexel University
Philadelphia
USA

ISSN 0255-0156 ISSN 2296-4878 (electronic)
ISBN 978-3-0348-0638-1 ISBN 978-3-0348-0639-8 (eBook)
DOI 10.1007/978-3-0348-0639-8
Springer Basel Heidelberg New York Dordrecht London
Library of Congress Control Number: 2013948131
Mathematics Subject Classification (2010): 47A68, 47B35, 39B42, 93B28, 15A15; 11C20, 47A13, 47A48

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Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Portrait of Leonid Lerer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Leonid Lerer’s Curriculum Vitae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Leonid Lerer’s List of Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
M.A. Kaashoek
Leonia Lerer’s Mathematical Work and Amsterdam Visits . . . . . . . . . . . 1
H. Bart
Leonia Lerer and My F irst Visit to Israel . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
I. Karelin
Through the Eyes of a Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
A.C.M. Ran
Reminiscences on Visits to Haifa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
H.J. Woerdeman
My F irst Research Experience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
J.A. Ball and V. Bolotnikov
Interpolation in Sub-Bergman Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
H. Bart, T. Ehrhardt and B. Silbermann
Zero Sums of Idempotents and Banach Algebras Failing
to be Spectrally Regular . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
T. Bella, Y. Eidelman, I. Gohberg, V. Olshevsky and E. Tyrtyshnikov
Fast Inversion of Polynomial-Vandermonde Matrices for
Polynomial Systems Related to Order One
Quasiseparable Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
vi Contents
H. Dym and M. Porat
Long Proofs of Two Carlson–Schneider Type Inertia Theorems . . . . . . 107
T. Ehrhardt and I.M. Spitkovsky
On the Kernel and Cokernel of Some Toeplitz Operators . . . . . . . . . . . . 127
A.E. Frazho, M.A. Kaashoek and A.C.M. Ran
Rational Matrix Solutions of a Bezout Type Equation
on the Half-plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
M.A. Kaashoek and F. van Schagen
Inverting Structured Operators Related to Toeplitz Plus
Hankel Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
P. Lancaster and I. Zaballa
On the Sign Characteristics of Selfadjoint Matrix Polynomials . . . . . . . 189
Yu.I. Lyubich
Quadratic Operators in Banach Spaces and Nonassociative
Banach Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
L. Rodman
Strong Stability of Invariant Subspaces of Quaternion Matrices . . . . . . 221
H.J. Woerdeman
Determinantal Representations of Stable Polynomials . . . . . . . . . . . . . . . 241
Preface
This volume is dedicated to Leonid Arie Lerer on the occasion of his seventieth
birthday (April 19, 2013). Leonia, as he is known to his friends, is an expert in the
theory of structured matrices and operators and related matrix-valued functions.
He has been a great inspiration to many.
Leonid Lerer started his mathematical career in Kishinev, Ukraine, with Alek
Markus and Israel Gohberg as research supervisors. He defended his Ph.D. thesis
in 1969 in Kharkov, Ukraine. In December 1973 he immigrated to Israel. Since
1981 he has been a professor at the Technion in Haifa where at present he has the
status of emeritus. He has educated six Ph.D. students and five masters students.
His more than 80 papers cover a wide spectrum of topics, ranging from functional
analysis and operator theory, linear and multilinear algebra, ordinary differential
equations, to systems and control theory.
This anniversary volume begins with a picture of Leonid Lerer, his Curricu-
lum Vitae and List of Publications, and personal notes written by former students,
mathematical friends and colleagues.
The main part of the book consists of a selection of peer-reviewed research
articles presenting recent results in areas that are close to Lerer’s mathematical
interests. This includes articles on Toeplitz, Wiener–Hopf, and Toeplitz plus Han-
kel operators, Bezout equations, inertia type results, matrix polynomials, in one
and severable variables, and related areas in matrix and operator theory.
We present this book to Leonid Lerer on behalf of all the authors as a token
of our respect and gratitude. We wish him many more years of good health and
happiness.
March 2013 Rien Kaashoek
Leiba Rodman
Hugo Woerdeman
Leonid Arie Lerer in an undated photograph
Operator Theory:
Advances and Applications, Vol. 237, ix–xii
⃝c 2013 Springer Basel
Leonid Lerer’s Curriculum Vitae
Date and place of birth: April 19, 1943; USSR
Date of immigration: December 1973
Marital status: Married, 2 children
Academic degrees
1965 M.Sc. Mathematics, Magna Cum Laude
Kishinev State University, Kishinev
1969 Ph.D. Mathematics
Physico-Technical Institute of Low Temperatures of the
Academy of Sciences of the Ukrainian SSR, Kharkov
Academic appointments
1969–73 Lecturer, Dept. of Physics and Mathematics
Kishinev State University
1974–75 Senior Researcher,
Technion Research & Development Foundation
Technion, Haifa
1975–80 Senior Lecturer, Dept. of Mathematics, Technion, Haifa
1981–88 Assoc. Professor, Dept. of Mathematics, Technion, Haifa
1988 (Feb.)– Full Professor, Dept. of Mathematics, Technion, Haifa
Visiting academic appointments
Visiting Professor, Dept. of Mathematics and Computer Science
at Vrije Universiteit, Amsterdam:
Feb. 1984–Feb. 1985, Mar.–Sept. 1990, Apr.–Nov. 2002,
Feb.–Apr. 2003, Jul.–Aug. 2003
Invited Guest, Dept. of Mathematics and Computer Science
at Vrije Universiteit, Amsterdam:
Jul.–Aug. 1978, 1980, 1982, 1983, 1985–93, 1995, 1996–97,
2000, 2004, Sept. 2005 (3–6 weeks each time)