Harmonic Analysis of Operators on Hilbert Space
The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Sinc
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Béla Sz.-Nagy • Ciprian Foias Hari Bercovici • László Kérchy
Harmonic Analysis of Operators on Hilbert Space Second Edition
Béla Sz.-Nagy (Deceased)
Ciprian Foias Mathematics Department Texas A & M University College Station, TX 77843-3368 USA [email protected]
Hari Bercovici Mathematics Department Indiana University Bloomington, IN 47405 USA [email protected]
László Kérchy Bolyai Institute Szeged University H-6720 Szeged Hungary [email protected]
Editorial Board: Sheldon Axler, San Francisco State University Vincenzo Capasso, Università degli Studi di Milano Carles Casacuberta, Universitat de Barcelona Angus MacIntyre, Queen Mary, University of London Kenneth Ribet, University of California, Berkeley Claude Sabbah, CNRS, École Polytechnique Endre Süli, University of Oxford Wojbor Woyczyński, Case Western Reserve University
ISBN 978-1-4419-6093-1 e-ISBN 978-1-4419-6094-8 DOI 10.1007/978-1-4419-6094-8 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010934634 Mathematics Subject Classification (2010): 47A45 Springer Science+Business Media, LLC 1970, 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Foreword
Sz.-Nagy and Foias had been planning for several years to issue an updated edition of their book Harmonic Analysis of Operators on Hilbert Space (North-Holland and Akad´emiai Kiad´o, Amsterdam–Budapest, 1970). This plan was not realized due to Sz.-Nagy’s death in 1998. Sz.-Nagy’s idea was to include all developments related to dilation theory and commutant lifting. Because there are several other volumes dedicated to some of these developments, we have decided to include in this volume only those subjects that are organically related to the original contents of the book. Thus, the study of C1· -contractions and their invariant subspaces in Chap. IX has its origins in Sec. VII.5, while the theory presented in Chap. X completes the study started in Secs. III.4 and IX.4 of the English edition. The material in the English edition has been reorganized to some extent. The material in the original Chaps. I–VIII was mostly preserved, but the results in the original Chap. IX were dispersed throughout the book. We have ad
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