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Perturbation theory for linear operators

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Authors:
  1. Tosio Kato

    1. University of California, Berkeley, USA

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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 132)

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-XIX
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  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 426-477

  10. Perturbation theory for semigroups of operators

    • Tosio Kato
    Pages 477-513

  11. Perturbation of continuous spectra and unitary equivalence

    • Tosio Kato
    Pages 514-565

  12. Erratum to: Operator Theory in Finite-Dimensional Vector Spaces

    • Tosio Kato
    Pages 591-591

  13. Erratum to: Introduction to the theory of operators in Banach spaces

    • Tosio Kato
    Pages 591-591

  14. Erratum to: Asymptotic perturbation theory

    • Tosio Kato
    Pages 591-591

  15. Erratum to: Perturbation theory in a finite-dimensional space

    • Tosio Kato
    Pages 591-591

  16. Erratum to: Operators in Hilbert spaces

    • Tosio Kato
    Pages 591-591

  17. Erratum to: Perturbation of continuous spectra and unitary equivalence

    • Tosio Kato
    Pages 591-592

  18. Back Matter

    Pages 566-590
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Keywords

About this book

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. 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 operators undergo a small change. Since its creation by RAY­ LEIGH and SCHRODINGER, 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 mathe­ matical 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).

Authors and Affiliations

  • University of California, Berkeley, USA

    Tosio Kato

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