Overview

Banach algebras combine algebraic and analytical aspects: it is the interplay of these structures that gives the subject its fascination. This volume expounds the general theory of Banach algebras, and shows how their topology is often determined by their algebraic structure: the central questions ask when homomorphisms and derivations from Banach algebras are automatically continuous, and seek canonical forms for these maps. The book synthesizes work over the last 20 years, and gives a definitive account; there are many new and unpublished results. The book describes many specific classes of Banach algebras, including function algebras, group algebras, algebras of operators, C*-algebras, and radical Banach algebras; it is a compendium of results on these examples. The subject interweaves algebra, functional analysis, and complex analysis, and has a dash of set theory and logic; the background in all these areas is fully explained. This volume is essential reading for anyone interested in any aspect of this vast subject.

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9780198500131

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This very comprehensive monograph represents a monumental work and a major achievement in the modern literature on Banach algebras and automatic continuity. Journal of Operator Theory This is a masterful exposition by one of the leading contributors to the field. For the worker in the area, the volume will be indispensable. Bulletin of the London Mathematical Society

This very comprehensive monograph represents a monumental work and a major achievement in the modern literature on Banach algebras and automatic continuity. Journal of Operator Theory This is a masterful exposition by one of the leading contributors to the field. For the worker in the area, the volume will be indispensable. Bulletin of the London Mathematical Society

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