Amenability of Convolution Algebras.
Copyright policy )Amenability of Convolution Algebras.
The amenability of the Banach algebra \(\ell^1(G)\) of a discrete semigroup \(G\), and its implications for the structure of \(G\) has been much studied over recent years. In this paper, we investigate implications of amenability of the algebras \(M(G)\), \(M(G)^{**}\) and \(LUC(G)^*\) on the structure of \(G\) for locally compact \(G\). The general thrust of the results is that taken together with mild algebraic hypotheses, such amenability necessitates that \(G\) satisfy some finiteness restrictions, and to be close to a group.
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510.mathematics, Banach algebra, amenability, discrete semigroup, convolution algebras, Structure, classification of topological algebras, Article, \(L^1\)-algebras on groups, semigroups, etc.
510.mathematics, Banach algebra, amenability, discrete semigroup, convolution algebras, Structure, classification of topological algebras, Article, \(L^1\)-algebras on groups, semigroups, etc.
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