© 1995

Perturbation Theory for Linear Operators


Part of the Classics in Mathematics book series (volume 132)

Table of contents

  1. Front Matter
    Pages I-XXI
  2. Tosio Kato
    Pages 189-250
  3. Tosio Kato
    Pages 251-308
  4. Tosio Kato
    Pages 364-426
  5. Tosio Kato
    Pages 426-479
  6. Back Matter
    Pages 568-623

About this book


In view of recent development in perturbation theory, supplementary notes and a supplementary bibliography are added at the end of the new edition. Little change has been made in the text except that the para­ graphs V-§ 4.5, VI-§ 4.3, and VIII-§ 1.4 have been completely rewritten, and a number of minor errors, mostly typographical, have been corrected. The author would like to thank many readers who brought the errors to his attention. Due to these changes, some theorems, lemmas, and formulas of the first edition are missing from the new edition while new ones are added. The new ones have numbers different from those attached to the old ones which they may have replaced. Despite considerable expansion, the bibliography i" not intended to be complete. Berkeley, April 1976 TosIO RATO Preface to the First Edition This book is intended to give a systematic presentation of perturba­ tion theory for linear operators. It is hoped that the book will be useful to students as well as to mature scientists, both in mathematics and in the physical sciences.


Excel Hilbert space Linear Operators differential equation differential operator field function functional functional analysis perturbation perturbation theory review ring theory scattering theory

Authors and affiliations

  1. 1.University of CaliforniaBerkeleyUSA

About the authors

Biography of Tosio Kato

Tosio Kato was born in 1917 in a village to the north of Tokyo. He studied theoretical physics at the Imperial University of Tokyo. After several years of inactivity during World War II due to poor health, he joined the Faculty of Science at the University of Tokyo in 1951. From 1962 he was Professor of Mathematics at the University of California, Berkeley, where he is now Professor Emeritus.

Kato was a pioneer in modern mathematical physics. He worked in te areas of operator theory, quantum mechanics, hydrodynamics, and partial differential equations, both linear and nonlinear.

Bibliographic information

  • Book Title Perturbation Theory for Linear Operators
  • Authors Tosio Kato
  • Series Title Classics in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-07558-5
  • Softcover ISBN 978-3-540-58661-6
  • eBook ISBN 978-3-642-66282-9
  • Series ISSN 1431-0821
  • Edition Number 2
  • Number of Pages XXI, 623
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published as volume 132 in the series: Grundlehren der mathematischen Wissenschaften
  • Topics Partial Differential Equations
    Calculus of Variations and Optimal Control; Optimization
  • Buy this book on publisher's site
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"The monograph by T. Kato is an excellent textbook in the theory of linear operators in Banach and Hilbert spaces. It is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
In chapters 1, 3, 5 operators in finite-dimensional vector spaces, Banach spaces and Hilbert spaces are introduced. Stability and perturbation theory are studied in finite-dimensional spaces (chapter 2) and in Banach spaces (chapter 4). Sesquilinear forms in Hilbert spaces are considered in detail (chapter 6), analytic and asymptotic perturbation theory is described (chapter 7 and 8). The fundamentals of semigroup theory are given in chapter 9. The supplementary notes appearing in the second edition of the book gave mainly additional information concerning scattering theory described in chapter 10.
The first edition is now 30 years old. The revised edition is 20 years old. Nevertheless it is a standard textbook for the theory of linear operators. It is user-friendly in the sense that any sought after definitions, theorems or proofs may be easily located. In the last two decades much progress has been made in understanding some of the topics dealt with in the book, for instance in semigroup and scattering theory. However the book has such a high didactical and scientific standard that I can recomment it for any mathematician or physicist interested in this field.
Zentralblatt MATH, 836