| Abstract: | Let ({mathcal {LM}}left( {mathcal {A}}, Pright) ) be an (ell ^1)-Munn algebra over an arbitrary unital Banach algebra ({mathcal {A}}). We characterize homomorphisms from ({mathcal {LM}}left( {mathcal {A}}, Pright) ) into an arbitrary Banach algebra ({mathcal {B}}) in terms of homomorphisms from ({mathcal {A}}) into ({mathcal {B}}). Then we discuss homomorphisms from arbitrary Banach algebras into ({mathcal {LM}}left( {mathcal {A}}, Pright) ). Existence and uniqueness of homomorphisms under certain conditions are also discussed. We apply these results to the concrete case of (ell ^1(S)) where S is a Rees matrix semigroup, to identify characters of (ell ^1(S)) in both cases where S is with or without zero. As a consequence if the sandwich matrix of S has a zero entry, then (ell ^1(S)) is character amenable. |
