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Banach Algebras on Semigroups and on Their Compactifications
H. G. Dales, University of Leeds, England, A. T.-M. Lau, University of Alberta, Edmonton, AB, Canada, and D. Strauss, University of Leeds, England

Memoirs of the American Mathematical Society
2010; 165 pp; softcover
Volume: 205
ISBN-10: 0-8218-4775-9
ISBN-13: 978-0-8218-4775-6
List Price: US$78
Individual Members: US$46.80
Institutional Members: US$62.40
Order Code: MEMO/205/966
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Let \(S\) be a (discrete) semigroup, and let \(\ell^{\,1}(S)\) be the Banach algebra which is the semigroup algebra of \(S\). The authors study the structure of this Banach algebra and of its second dual.

The authors determine exactly when \(\ell^{\,1}(S)\) is amenable as a Banach algebra, and shall discuss its amenability constant, showing that there are `forbidden values' for this constant.

Table of Contents

  • Introduction
  • Banach algebras and their second duals
  • Semigroups
  • Semigroup algebras
  • Stone-Čech compactifications
  • The semigroup \((\beta S, \Box)\)
  • Second duals of semigroup algebras
  • Related spaces and compactifications
  • Amenability for semigroups
  • Amenability of semigroup algebras
  • Amenability and weak amenability for certain Banach algebras
  • Topological centres
  • Open problems
  • Bibliography
  • Index of terms
  • Index of symbols
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