APPROXIMATE AMENABILITY OF CERTAIN INVERSE SEMIGROUP ALGEBRAS

doi:10.1016/S0252-9602(13)60020-X

Abstract

Abstract:

In this article, the approximate amenability of semigroup algebra ?1(S) is in-vestigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup S, the notions of amenability, approximate amenability and bounded approximate amenability of ?1(S) are equivalent. We use this to give a direct proof of the approximate amenability of ?1(S) for a Brandt semigroup S. More-over, we characterize the approximate amenability of ?1(S), where S is a uniformly locally finite band semigroup.

Key words: Approximate amenability, semigroup algebras, uniformly locally finite inverse semigroup, Brandt semigroup

CLC Number:

43A20

Mehdi ROSTAMI, Abdolrasoul POURABBAS, Morteza ESSMAILI. APPROXIMATE AMENABILITY OF CERTAIN INVERSE SEMIGROUP ALGEBRAS[J].Acta mathematica scientia,Series B, 2013, 33(2): 565-577.

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