On the existence of an ultra central approximate identity for certain semigroup algebras

Abstract

In this paper we characterize the existance of an ultra central approximate identity for ${\ell }^1(S)$, where $S$ is a uniformly locally finite inverse semigroup. As an application, for the Brandt semigroup $S=M^0(G,I)$ over a non-empty set $I$, we show that ${\ell }^1(S)$ has an ultra central approximate identity if and only if $I$ is finite.