On pseudo-amenability of commutative semigroup algebras and their second duals |
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Authors: | Email author" target="_blank">M?SoroushmehrEmail author M?Rostami M?Essmaili |
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Institution: | 1.Mosaheb Institue of Mathematics,Kharazmi University,Tehran,Iran;2.Faculty of Mathematical and Computer Science,Amirkabir University of Technology,Tehran,Iran;3.Faculty of Mathematical and Computer Sciences,Kharazmi University,Tehran,Iran |
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Abstract: | In this paper, we first characterize pseudo-amenability of semigroup algebras \(\ell ^1(S),\) for a certain class of commutative semigroups S, the so-called archimedean semigroups. We show that for an archimedean semigroup S, pseudo-amenability, amenability and approximate amenability of \(\ell ^1(S)\) are equivalent. Then for a commutative semigroup S, we show that pseudo-amenability of \(\ell ^{1}(S)\) implies that S is a Clifford semigroup. Finally, we give some results on pseudo-amenability and approximate amenability of the second dual of a certain class of commutative semigroup algebras \(\ell ^1(S)\). |
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