Skip to main content
SpringerLink
Log in
Book cover

Perturbation Theory for Linear Operators

  • Book
  • © 1995

Overview

Authors:
  1. Tosio Kato

    1. University of California, Berkeley, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (10 chapters)

  1. Front Matter

    Pages I-XXI
    Download chapter PDF

  2. Operator theory in finite-dimensional vector spaces

    • Tosio Kato
    Pages 1-62

  3. Perturbation theory in a finite-dimensional space

    • Tosio Kato
    Pages 62-126

  4. Introduction to the theory of operators in Banach spaces

    • Tosio Kato
    Pages 126-188

  5. Stability theorems

    • Tosio Kato
    Pages 189-250

  6. Operators in Hilbert spaces

    • Tosio Kato
    Pages 251-308

  7. Sesquilinear forms in Hilbert spaces and associated operators

    • Tosio Kato
    Pages 308-364

  8. Analytic perturbation theory

    • Tosio Kato
    Pages 364-426

  9. Asymptotic perturbation theory

    • Tosio Kato
    Pages 426-479

  10. Perturbation theory for semigroups of operators

    • Tosio Kato
    Pages 479-515

  11. Perturbation of continuous spectra and unitary equivalence

    • Tosio Kato
    Pages 516-567

  12. Back Matter

    Pages 568-623
    Download chapter PDF
Back to top

Keywords

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.

Reviews

"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

Authors and Affiliations

  • University of California, Berkeley, USA

    Tosio Kato

About the author

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: https://doi.org/10.1007/978-3-642-66282-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1995

  • Softcover ISBN: 978-3-540-58661-6Published: 15 February 1995

  • eBook ISBN: 978-3-642-66282-9Published: 06 December 2012

  • Series ISSN: 1431-0821

  • Series E-ISSN: 2512-5257

  • Edition Number: 2

  • Number of Pages: XXI, 623

  • 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

Publish with us

Policies and ethics

Back to top

Search

Navigation