© 2020

Amenable Banach Algebras

A Panorama


Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Volker Runde
    Pages 1-19
  3. Volker Runde
    Pages 21-55
  4. Volker Runde
    Pages 57-96
  5. Volker Runde
    Pages 97-149
  6. Volker Runde
    Pages 151-199
  7. Volker Runde
    Pages 201-257
  8. Volker Runde
    Pages 259-283
  9. Volker Runde
    Pages 285-342
  10. Volker Runde
    Pages 343-363
  11. Back Matter
    Pages 365-462

About this book


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.


Amenability book Amenability research Amenability Runde Amenable Banach algebras Banach algebras book Operator algebras on Hilbert spaces Functional analysis Abstract harmonic analysis Von Neumann algebra Operators Banach spaces Locally compact groups Weak amenability Dual Banach algebras

Authors and affiliations

  1. 1.Department of Mathematical and Statistical ScienceUniversity of AlbertaEdmontonCanada

About the authors

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.

Bibliographic information

  • Book Title Amenable Banach Algebras
  • Book Subtitle A Panorama
  • Authors Volker Runde
  • Series Title Springer Monographs in Mathematics
  • Series Abbreviated Title Springer Monographs in Mathematics
  • DOI
  • Copyright Information Springer Science+Business Media, LLC, part of Springer Nature 2020
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-0716-0349-9
  • eBook ISBN 978-1-0716-0351-2
  • Series ISSN 1439-7382
  • Series E-ISSN 2196-9922
  • Edition Number 1
  • Number of Pages XVII, 462
  • Number of Illustrations 34 b/w illustrations, 0 illustrations in colour
  • Topics Functional Analysis
    Abstract Harmonic Analysis
    Operator Theory
  • Buy this book on publisher's site
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“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)