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

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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 © Springer Basel 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer Basel is part of Springer Science+Business Media (www.birkhauser-science.com) 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)

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