Banach Function Algebras, Arens Regularity, and BSE Norms

Harold Garth Dales, Ali Ülger

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English

Springer International Publishing AG
20 February 2024

Algebra; Functional analysis & transforms; Integral calculus & equations

Series: CMS/CAIMS Books in Mathematics

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.

By: Harold Garth Dales, Ali Ülger
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 2024 ed.
Volume: 12
Dimensions: Height: 235mm, Width: 155mm,
Weight: 847g
ISBN: 9783031445316
ISBN 10: 3031445317
Series: CMS/CAIMS Books in Mathematics
Pages: 445
Publication Date: 20 February 2024
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Reviews for Banach Function Algebras, Arens Regularity, and BSE Norms

“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)