Duality theorem for topological semigroups

Abstract

For topological semigroups $S$, we consider Tannaka-type duality theorems, which are extensions of the notion of weak Tannaka duality theorem for topological groups. In the case of topological semigroups, we must set as the dual object of $S$ all isometric representations of $S$ instead of all unitary representations. We define a property T-type for $S$. After arguments analogous to previous work from the author, we can prove that our Tannaka-type duality theorem is valid if and only if $S$ is a T-type semigroup.