Fredholm and Local Spectral Theory II With Application to Weyl-type
This monograph concerns the relationship between the local spectral theory and Fredholm theory of bounded linear operators acting on Banach spaces. The purpose of this book is to provide a first general treatment of the theory of operators for which Weyl-
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Pietro Aiena
Fredholm and Local Spectral Theory II With Application to Weyl-type Theorems
Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Board: Michel Brion, Grenoble Camillo De Lellis, Princeton Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Pietro Aiena
Fredholm and Local Spectral Theory II With Application to Weyl-type Theorems
123
Pietro Aiena Dipartimento di Matematica Universit`a degli Studi di Palermo Palermo, Italy
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-030-02265-5 ISBN 978-3-030-02266-2 (eBook) https://doi.org/10.1007/978-3-030-02266-2 Library of Congress Control Number: 2018962161 Mathematics Subject Classification (2010): 47A05, 47A10, 47A11, 47A53 © Springer Nature Switzerland AG 2018 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 Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
A mia moglie Maria, ai miei figli Marco, Caterina, Adriana, e a tutti i miei cari familiari
Preface
The main focus of this book is on bounded linear operators on complex infinitedimensional Banach spaces and their spectral properties. In recent years spectral theory, which has numerous and important applications in many parts of modern analysis and physics, has witnessed considerable development. In this book the reader is assumed to be familiar with the basic notions of linear algebra, functional analysis and complex analysis. Essentially, the aim of this book is to give an idea of the relationship between local spectral the
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