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9783540035268

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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.<br>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.<br>The first edition is now 30 years old. The revised edition is 20 years old. Nevertheless it is a stan

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