The Elements of Operator Theory
"The author endeavors to present the concepts and ideas as an alternative to the computational approach, trying to avoid long calculations by stressing the mathematical thoughts behind the statements. . . . many problems [are] stated throughout the book,
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The Elements of Operator Theory Second Edition
Carlos S. Kubrusly
The Elements of Operator Theory Second Edition
Carlos S. Kubrusly Electrical Engineering Department Catholic University of Rio de Janeiro R. Marques de S. Vicente 225 22453-900, Rio de Janeiro, RJ, Brazil [email protected]
ISBN 978-0-8176-4997-5 e-ISBN 978-0-8176-4998-2 DOI 10.1007/978-0-8176-4998-2 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011922537 Mathematics Subject Classification (2010): 47-01, 47A-xx, 47B-xx, 47C-xx, 47D-xx, 47L-xx © Springer Science+Business Media, LLC 2011 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 www.birkhauser-science.com
To the memory of my father
The truth, he thought, has never been of any real value to any human being — it is a symbol for mathematicians and philosophers to pursue. In human relations kindness and lies are worth a thousand truths. He involved himself in what he always knew was a vain struggle to retain the lies. Graham Greene
Preface to the Second Edition
This is a revised, corrected, enlarged, updated, and thoroughly rewritten version for a second edition of Elements of Operator Theory (Birkh¨auser, Boston, 2001). Although a considerable amount of new material has been added to this new edition, it was not altered in a significant way: the original focus and organization were preserved. In particular, the numbering system of the former edition (concerning chapters, sections, definitions, propositions, lemmas, theorems, corollaries, examples, and problems) has been kept. New material was either embedded in the text without changing those numbers (to catch up with the previous edition for reference purposes so that citations made to the previous edition still hold for the new edition) or included at the end of each chapter with a subsequent numbering. All problems and references of the first edition have also been kept, and 33 new problems and 24 new references (22 books and 2 papers) were added to the present edition. The logical dependence of the various sections (and chapters) is roughly linear and reflects approximately the minimum amount of material needed to proceed further. A few parts might be compressed or even skipped in a first reading. Chapter 1 may be taken for self-study (and an important one at that), and a formal course of lectures might
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