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Table of contents (10 chapters)
Reviews
In chapters 1, 3, 5 operators in finitedimensional vector spaces, Banach spaces and Hilbert spaces are introduced. Stability and perturbation theory are studied in finitedimensional 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 userfriendly 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
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/10.1007/9783642662829
Publisher: Springer Berlin, Heidelberg

eBook Packages: Springer Book Archive
Copyright Information: SpringerVerlag Berlin Heidelberg 1995
Softcover ISBN: 9783540586616Published: 15 February 1995
eBook ISBN: 9783642662829Published: 06 December 2012
Series ISSN: 14310821
Series EISSN: 25125257
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