The topological centers of LUC(S)* and M a (S)** of certain foundation semigroups

Abstract

In the present paper, for a large family of topological semigroups namely, compactly cancellative and right cancellative foundation semigroups S, we study the topological centers of the Banach algebras LUC(S)* and M a S**. We also give a generalization of a known result of Lau and Lorsert by showing that for such topological semigroups the topological center of LUC(S)* (M a S**, respectively) is the same as MS (M a S, respectively).