Banach Algebra Structure and Amenability of a Class of Matrix Algebras with Applications

We introduce a new category of Banach algebras, ℓ1-Munn algebras which we use as a tool in the study of semigroup algebras. Then we characterize amenable ℓ1-Munn algebras and also semisimple ones in this category. Applying these results to the semigroup algebras provides some characterizations of amenable semigroup algebras. We also provide a counter example to a conjecture of Duncan and Paterson.