Pseudo-contractibility and pseudo-amenability of semigroup algebras

Abstract

In this paper, we characterize pseudo-contractibility of 1 (S), where S is a uniformly locally finite inverse semigroup. As a consequence, we show that for a Brandt semigroup S = M 0 (G, I), the semigroup algebra 1 (S) is pseudo-contractible if and only if G and I are finite. Moreover, we study the notions of pseudo-amenability and pseudo-contractibility of a semigroup algebra 1 (S) in terms of the amenability of S. Mathematics Subject Classification (2000). Primary 43A20, 20M18; Secondary 16E40.

Pseudo-amenability and pseudo-contractibility of restricted semigroup algebra

“…Suppose l 1 (S r ) is pseudo-amenable and l 1 (S) = l 1 (S r ) as in the above argument, G is amenable [8,Corollary 3.8]. Hence G and I are finite and so by Corollary 2.5 [7], l 1 (S r ) is pseudo-contractible.…”

“…By Example 1.2 in [14], S = S r and so l 1 (S) = l 1 (S r ). Now suppose l 1 (S r ) is pseudo-contractible, then G and I are finite [7,Corollary 2.5].…”

“…The notions of pseudo-amenability and pseudo-contractibility in Banach algebra which were introduced in [9], have been studied for different classes of semigroups. The notable ones among these are the research work in [7], [8] and [19]. The authors in [7] particularly showed that for a Brandt semigroup S = M 0 (G, I), the semigroup algebra l 1 (S) is pseudo-contractible if and only G and I are finite.…”

“…The notable ones among these are the research work in [7], [8] and [19]. The authors in [7] particularly showed that for a Brandt semigroup S = M 0 (G, I), the semigroup algebra l 1 (S) is pseudo-contractible if and only G and I are finite.…”

Counter examples for pseudo-amenability of some semigroup algebras

“…Pseudo-amenability of some Banach algebras like Segal algebras, semigroup algebras and matrix algebras were investigated in [6], [7], [13] and [5].…”