Weighted Semigroup Algebras as Dual Banach Algebras

Abstract

A dual Banach algebra is a Banach algebra which is a dual space, and its multiplication is separately $$w^*$$-continuous. Among other things, the main objective of this paper is to study those conditions under which the weighted semigroup algebra $$l^1(S,\omega )$$ is a dual Banach algebra with predual $$c_0(S)$$. Moreover, our results illustrated how the properties of a weight function could lead to a different behavior from that of $$l^1(S)$$ as dual Banach algebras.