Memoirs of the American Mathematical Society 2010; 165 pp; softcover Volume: 205 ISBN10: 0821847759 ISBN13: 9780821847756 List Price: US$78 Individual Members: US$46.80 Institutional Members: US$62.40 Order Code: MEMO/205/966
 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
 StoneČech 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
