On Munn Projective Tensor Product Algebras and Connes Amenability

Abstract

. In this paper, we study and investigate Connes amenability for l 1 -Munn algebra LM(A⊗Bb ; P, I, J) where A and B are Banach algebras, I and J are nonempty sets and P is invertible matrix. Then we use the obtained results to semigroup algebras l 1 (S⊗bT) that S and T are semigroups. Also, we prove that if S⊗bT is a weakly cancellative semigroup and l 1 (S⊗bT) be Connes amenable then the idempotents set of S⊗bT will be finite