Operator Functions and Localization of Spectra

Michael I. Gil’ (auth.)3540202463, 9783540202462

“Operator Functions and Localization of Spectra” is the first book that presents a systematic exposition of bounds for the spectra of various linear nonself-adjoint operators in a Hilbert space, having discrete and continuous spectra. In particular bounds for the spectra of integral, differential and integro-differential operators, as well as finite and infinite matrices are established. The volume also presents a systematic exposition of estimates for norms of operator-valued functions and their applications.

Table of contents :
1 Preliminaries….Pages 1-9
2 Norms of Matrix-Valued Functions….Pages 11-34
3 Invertibility of Finite Matrices….Pages 35-48
4 Localization of Eigenvalues of Finite Matrices….Pages 49-63
5 Block Matrices and π -Triangular Matrices….Pages 65-74
6 Norm Estimates for Functions of Compact Operators in a Hilbert Space….Pages 75-96
7 Functions of Non-compact Operators….Pages 97-121
8 Bounded Perturbations of Nonselfadjoint Operators….Pages 123-134
9 Spectrum Localization of Nonself-adjoint Operators….Pages 135-149
10 Multiplicative Representations of Resolvents….Pages 151-161
11 Relatively P -Triangular Operators….Pages 163-172
12 Relatively Compact Perturbations of Normal Operators….Pages 173-180
13 Infinite Matrices in Hilbert Spaces and Differential Operators….Pages 181-188
14 Integral Operators in Space L 2 ….Pages 189-197
15 Operator Matrices….Pages 199-213
16 Hille – Tamarkin Integral Operators….Pages 215-226
17 Integral Operators in Space L ℞ ….Pages 227-234
18 Hille – Tamarkin Matrices….Pages 235-241
19 Zeros of Entire Functions….Pages 243-252