Spectral Theory of Bounded Linear Operators

This textbook introduces spectral theory for bounded linear operators by focusing on (i) the spectral theory and functional calculus for normal operators acting on Hilbert spaces; (ii) the Riesz-Dunford functional calculus for Banach-space operators; and

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Spectral Theory of Bounded Linear Operators

Carlos S. Kubrusly

Spectral Theory of Bounded Linear Operators

Carlos S. Kubrusly Institute of Mathematics Federal University of Rio de Janeiro Rio de Janeiro, Brazil

ISBN 978-3-030-33148-1 ISBN 978-3-030-33149-8 (eBook) https://doi.org/10.1007/978-3-030-33149-8 Mathematics Subject Classification (2010): 47-00, 47-01, 47-02, 47A10, 47A12, 47A16, 47A25, 47A53, 47A60, 47B15, 47B20, 47B48, 47C05 © Springer Nature Switzerland AG 2020 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. 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. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To Alan and Jessica

The positivists have a simple solution: the world must be divided into that which we can say clearly and the rest, which we had better pass over in silence. But can anyone conceive of a more pointless philosophy, seeing that what we can say clearly amounts to next to nothing? If we omitted all that is unclear, we would probably be left with completely uninteresting and trivial tautologies. Werner Heisenberg [62, Chapter 17, p. 213]

Mathematics is not a language, it’s an adventure. [...] Most mathematics is done with a friend over a cup of coffee, with a diagram scribbled on a napkin. Mathematics is and always has been about ideas, and a valuable idea transcends the symbols with which you choose to represent it. As Carl Friedrich Gauss once remarked, “What we need are notions, not notations.” Paul Lockhart [92, Part I, p. 53]

Preface

The book introduces spectral theory for bounded linear operators, giving a modern text for a graduate course focusing on two basic aspects. On the one hand, the spectral theory for normal operators acting on Hilbert spaces is comprehensively investigated, emphasizing rece