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