Overview

This book shows the deep interaction between two important theories: Fredholm and local spectral theory. A particular emphasis is placed on the applications to multipliers and in particular to convolution operators. The book also presents some important progress, made in recent years, in the study of perturbation theory for classes of operators which occur in Fredholm theory.

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9781402018305

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From the reviews of the first edition: <p> The primary goal of this monograph is a presentation of the Fredholm and Riesz theory of Banach space operators and applications in the stetting of multipliers of a commutative Banach algebra. a ] This book complements standard references for Fredholm theory a ] on the one hand, and Laursen and Neumanna (TM)s book on the other hand. It should prove to be a valuable resource for graduate students and researchers in Banach space operator theory. (Thomas Len Miller, Mathematical Reviews, 2005e) <p> The main concern of the monograph under review is Fredholm theory and its connections with the local spectral theory for bounded linear operators in Banach spaces. a ] The monograph is intended for the use of researchers and graduate students in functional analysis, having a certain background in operator theory. The style is alert and pleasant and there is a fair and state-of-the-art account of the actual Fredholm theory in connection with local spectral theory. (Florian-Horia Vasilescu, Zentralblatt MATH, Vol. 1077 (3), 2006)

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