APPROXIMATE AMENABILITY OF CERTAIN INVERSE SEMIGROUP ALGEBRAS

In this article, the approximate amenability of semigroup algebra 1(S) is investigated, 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. Moreover, we characterize the approximate amenability of 1(S), where S is a uniformly locally finite band semigroup.