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This book is about semisimple Banach algebras with a focus on those that are commutative.
After laying out the necessary background material from functional analysis, geometry of Banach spaces and measure theory, we introduce many specific Banach algebras from operator theory, harmonic analysis, and function theory and study their basic properties.
Some of the questions dealt with in the book are: Whether the introduced Banach algebras are BSE-algebras, whether they have BSE norms, whether they have the separating ball property or some variant of it, and whether they are Arens regular. The book contains quite a few new results, as well as new proofs of a good many known results.
The book is intended for those who are preparing to work in Banach algebras or who have been doing research in related areas.
List of contents
Banach spaces and operators.- Banach algebras.- Banach function algebras.- Banach algebras on locally compact groups.- BSE norms and BSE algebras.- Arens regularity.
Report
"The book is extremely rich in the results displayed. ... This allows the authors to cover a tremendous amount of material which makes the volume not only interesting for specialists, but also a reference text suitable for a wider audience. Specialists and nonspecialists alike will agree that this text is a pleasure to read." (Dirk Werner, zbMATH 1546.46002, 2024)
