Banach Algebras on Semigroups and on Their Compactifications (Memoirs of the American Mathematical Society)
Banach Algebras on Semigroups and on Their Compactifications (Memoirs of the American Mathematical Society) by H. G. Dales
English | 2010 | ISBN: 0821847759 | 165 Pages | PDF | 1.24 MB
English | 2010 | ISBN: 0821847759 | 165 Pages | PDF | 1.24 MB
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-?ech 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. (MEMO/205/966)