Perturbation theory for linear operators
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Herausgegeben von
J. L. Doob · E. Heinz · F. Hirzebruch · E. Hopf H. Hopf · W. Maak · S. Mac Lane W. Magnus · D. Mumford · F. K. Schmidt · K. Stein
Geschäftsführende Herausgeber B. Eckmann und B. L. van der W aerden
Perturbation theory for linear operators
Dr. Tosio Kato Professor of Mathematics University of California, Berkeley
With 3 Figures
Springer Science+Business Media, LLC 1966
Geschăftsfilhrende
Herausgeber:
Prof. Dr. B. Eckmann Eidgenăssische
Technische Hochschule Zilrich
Prof. Dr. B. L. van der Waerden Mathematisches Institut der Universitat Ziirich
Ali rights reserved, especially that of translation into foreign languages It is also forbidden to reproduce this book, either whole or in part, by photomechanical means ( photostat, microfilm and/or microcard or any other means) wirhout written permission from the Publishers © 1966 by Springer Science+Business Media New York Originally published by Springer-Verlag New York Inc. in 1966 Softcover reprint of the hardcover 1st edition 1966 Library of Congress Catalog Card Number 66-15274 ISBN 978-3-662-12680-6 ISBN 978-3-662-12678-3 (eBook) DOI 10.1007/978-3-662-12678-3
Title No. 5115
To the memory of my parents
Preface This book is intended to give a systematic presentation of perturbation theory for linear operators. It is hoped that the book will be useful to students as well as to mature scientists, bothin mathematics andin the physical sciences. Perturbation theory for linear operators is a collection of diversified results in the spectral theory of linear operators, unified more or less loosely by their common concern with the behavior of spectral properties when the operatorsundergo a small change. Since its creation by RAYLEIGH and ScHRÖDINGER, the theory has occupied an important place in applied mathematics; during the last decades, it has grown into a mathematical discipline with its own interest. The book aims at a mathematical treatment of the subject, with due consideration of applications. The mathematical foundations of the theory belong to functional analysis. But since the book is partly intended for physical scientists, who might lack training in functional analysis, not even the elements of that subject are presupposed. The reader is assumed to have only a basic knowledge of linear algebra and real and complex analysis. The necessary tools in functional analysis, which are restricted to the most elementary part of the subject, are developed in the text as the need for them arises (Chapters I, III and parts of Chapters V, VI). An introduction, containing abrief historical account of the theory, precedes the main exposition. There are ten chapters, each prefaced by a summary. Chapters are divided into sections, and sections into paragraphs. I-§ 2.3, for example, means paragraph three of section two of chapter one; it is simply written § 2.3 when referred to within the same chapter and par. 3 when referred to within the same section. Theorems, Corollaries, Lemmas, Remarks, Problems, and Examples are numbered in one list within
