The Banach algebras generated by representations of abelian semigroups

摘要

Let S be a suitable subsemigroup of a locally compact abelian group. We consider the class of Banach algebras A for which there exists a continuous homomorphism ω : L 1 (S) → A with dense range. We study the behavior of the radical in such algebras. As an application, we present some results concerning the structure of weakly compact homomorphisms of semigroup algebras.