A characterization of the $L^{\infty}$-representation algebra $\mathfrak{R}(S)$ of a foundation semigroup and its application to BSE algebras

Abstract

For a locally compact Hausdorff semigroup $S$, the $L^{\infty}$-representation algebra $\mathfrak{R}(S)$ was extensively studied by Dunkl and Ramirez. In this paper we give a characterization of the Banach algebra $\mathfrak{R}(S)$ of a foundation semigroup $S$ and as an application we determine some BSE semigroup algerbras.