Completely continuous linear maps on semigroup algebras

For a locally compact group G, L1(G) is its group algebra and L?(G) is the dual of L1(G). Crombez and Govaerts introduced the notion of a uniformly measurable function in L?(G) and proved that such a function induces a completely continuous operator. The aim of this paper is to go further and generalize the above results to foundation semigroup algebras. We study completely continuous linear maps on semigroup algebras which commute with translations.