Volume 36 • Number 1 • 2013   • Completely Continuous Linear Maps on Semigroup Algebra Ali Ghaffari Abstract. For a locally compact group $G$, $L^1(G)$ is its group algebra and $L^\infty(G)$ is the dual of $L^1(G)$. Crombez and Govaerts introduced the notion of a uniformly measurable function in $L^\infty(G)$ 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. 2010 Mathematics Subject Classification: Primary: 43A22; Secondary: 43A60 Full text: PDF