Amenable Banach Algebras: A Panorama

ISBN-13: 9781071603499 / Angielski / Twarda / 2020 / 462 str.

Volker Runde

Recenzje

"The author gives full and complete proofs of many significant theorems. This book is indeed a 'panorama' on the subject of amenable Banach algebras. ... The notes and comments at the end of chapters appear to be remarkably accurate and comprehensive in citing the literature; the author appears to have a complete knowledge of the history of existing papers. The notes include some open problems." (H. G. Dales, Mathematical Reviews, May, 2022)

"This book is written in a clear and readable style. ... Graduate students and researchers in the theory of Banach and operator algebras will enjoy reading this carefully written book." (Mohammad Sal Moslehian, zbMATH 1445.46001, 2020)

Spis treści

Preface.- List of Symbols.- Introduction.- 0 Paradoxical Decompositions.- 1 Amenable, Locally Compact Groups.- 2 Amenable Banach Algebras.- 3 Examples.- 4 Amenability-Like Properties.- 5 Dual Banach Algebras.- 6 Banach Homological Algebra.- 7 Operator Algebras on Hilbert Spaces.- 8 Operator Amenability.- A Banach Spaces.- B Banach Algebras.- C C*- and Neumann Algebras.- D Abstract Harmonic Analysis.- E Operator Spaces.- F Fourier and Fourier-Stieltjes Algebras.- References.- Index​ of Names.- Index.

O autorze

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.

Blurb

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.