HOMOMORPHISMS OF -MUNN ALGEBRAS AND APPLICATIONS TO SEMIGROUP ALGEBRAS

Abstract

In this paper, for an arbitrary$\ell ^{1}$-Munn algebra$\mathfrak{A}$over a Banach algebra$A$with a sandwich matrix$P$, we characterise all homomorphisms from$\mathfrak{A}$to a commutative Banach algebra$B$. Especially, we study the character space of this algebra. Then, as an application, its character amenability is investigated. Finally, we apply these results to certain semigroups, which are called Rees matrix semigroups.