Pseudo-amenability of Brandt semigroup algebras
نویسنده
چکیده
The concept of amenability for Banach algebras was introduced by Johnson in 1972 [6]. Several modifications of this notion, such as approximate amenability and pseudo-amenability, were introduced in [2] and [4]. In the current paper we investigate the pseudo-amenability of Brandt semigroup algebras. It was shown in [2] and [4] that for the group algebra L(G), amenability, approximate amenability and pseudo-amenability coincide and are equivalent to the amenability of locally compact group G. In the semigroup case we know that, if S is a discrete semigroup, then amenability of l(S) implies that S is regular and amenable [1]. Ghahramani et al. [3] have shown that, if l(S) is approximately amenable, then S is regular and amenable. The present author and Pourabbas in [9] have shown that for a Brandt semigroup S over a group G with an index set I, the following are equivalent. (i) l(S) is amenable. (ii) l(S) is approximately amenable. (iii) I is finite and G is amenable. This result corrects [7, Theorem 1.8]. In the present paper we show that for a Brandt semigroup S over a group G with an arbitrary (finite or infinite) index set I, amenability of G implies pseudo-amenability of l(S).
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