Amenable Banach Algebras

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.

“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)

• 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.