This authoritative text presents a broad view of the spectral theory of non-self-adjoint linear operators and contains many illustrative examples and exercises. Topics discussed include Fredholm theory, Hilbert-Schmidt and trace class operators, one-parameter semigroups, perturbations of their generators and a thorough account of the new theory of pseudospectra.

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'One will look in vain for the notions of pseudospectrum, hull and numerical range in standard functional analysis texts, so Davies has done us a great service by explaining them through beautiful theorems and examples. More generally, his book is the first to offer a comprehensive survey of the spectral theory of non-self-adjoint operators, including both 'classical' and 'cutting edge' results, showing that this theory holds as much promise as the self-adjoint theory in both foundations and application. The scope of the book is truly enormous and is only partly reflected by listing the chapter titles ... [a] beautiful volume, which has no competitors.' The Mathematical Intelligencer

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Linear Operators and Their Spectra

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