Arens regularity and point Arens regularity of semigroup algebras

Abstract

The purpose of this article is to study the concepts Arens regularity for semigroup algebras $$M_a(S)$$ , $$\ell ^1(S)$$ , and $${ LUC}(S)^*$$ . We give a necessary and sufficient condition for $$M_a(S)$$ to be pointwise Arens regular. We then give some characterizations for Arens regularity of $$M_a(S)$$ and $$\ell ^1(S)$$ . Also, we investigate weakly compact multipliers on $$M_a(S)$$ and then for a compactly cancellative foundation semigroup S with identity, we show that S is compact if $${ LUC}(S)^*$$ is Arens regular.