This book is about semisimple Banach algebras with a focus on those that are commutative. 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.
Banach spaces and operators.- Banach algebras.- Banach function algebras.- Banach algebras on locally compact groups.- BSE norms and BSE algebras.- Arens regularity.
“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)