Amenable Banach Algebras: A Panorama (Springer Monographs in Mathematics) - Hardcover

Runde, Volker

Hardcover

ISBN 10: 1071603493 ISBN 13: 9781071603499

Publisher: Springer, 2020

Synopsis

This volume provides readers with a detailed introduction to the amenability of Banach algebras and locally compact groups. By encompassing important foundational material, contemporary research, and recent advancements, this monograph offers a state-of-the-art reference. It will appeal to anyone interested in questions of amenability, including those familiar with the author’s previous volume Lectures on Amenability.

Cornerstone topics are covered first: namely, the theory of amenability, its historical context, and key properties of amenable groups. This introduction leads to the amenability of Banach algebras, which is the main focus of the book. Dual Banach algebras are given an in-depth exploration, as are Banach spaces, Banach homological algebra, and more. By covering amenability’s many applications, the author offers a simultaneously expansive and detailed treatment. Additionally, there are numerous exercises and notes at the end of every chapter that further elaborate on the chapter’s contents.

Because it covers both the basics and cutting edge research, Amenable Banach Algebras will be indispensable to both graduate students and researchers working in functional analysis, harmonic analysis, topological groups, and Banach algebras. Instructors seeking to design an advanced course around this subject will appreciate the student-friendly elements; a prerequisite of functional analysis, abstract harmonic analysis, and Banach algebra theory is assumed.

About this title

About the Author

Volker Runde obtained his Diplom at Münster (Germany), his PhD at UC Berkeley, and the Habilitation at Saarbrücken (Germany). Since 1999, he has been a professor of mathematics at the University of Alberta. His research centers around Banach algebras, their rôle in abstract harmonic analysis and, in particular, the phenomenon of amenability. Among his previous books are the popular Lectures on Amenability, of which the present volume is a greatly expanded update.

From the Back Cover

This volume provides readers with a detailed introduction to the amenability of Banach algebras and locally compact groups. By encompassing important foundational material, contemporary research, and recent advancements, this monograph offers a state-of-the-art reference. It will appeal to anyone interested in questions of amenability, including those familiar with the author’s previous volume Lectures on Amenability.

Cornerstone topics are covered first: namely, the theory of amenability, its historical context, and key properties of amenable groups. This introduction leads to the amenability of Banach algebras, which is the main focus of the book. Dual Banach algebras are given an in-depth exploration, as are Banach spaces, Banach homological algebra, and more. By covering amenability’s many applications, the author offers a simultaneously expansive and detailed treatment. Additionally, there are numerous exercises and notes at the end of every chapter that furtherelaborate on the chapter’s contents.

Because it covers both the basics and cutting edge research, Amenable Banach Algebras will be indispensable to both graduate students and researchers working in functional analysis, harmonic analysis, topological groups, and Banach algebras. Instructors seeking to design an advanced course around this subject will appreciate the student-friendly elements; a prerequisite of functional analysis, abstract harmonic analysis, and Banach algebra theory is assumed.

Edition details

• Publisher: Springer
• Publication date: 2020
• Language: English
• ISBN 10: 1071603493
• ISBN 13: 9781071603499
• Binding: Hardcover
• Edition number: 1
• Number of pages: 479