SYMMETRIC MODULE AND CONNES AMENABILITY

In this paper we introduce two symmetric variants ofamenability, symmetric module amenability and symmetric Connesamenability. We determine symmetric module amenability andsymmetric Connes amenability of some concrete Banach algebras.Indeed, it is shown that ℓ1(S) is a symmetric ℓ1(E)-module amenableif and only if S is amenable, where S is an inverse semigroup withsubsemigroup E(S) of idempotents. In symmetric connes amenability, we have proved that M(G) is symmetric connes amenable if andonly if G is amenable.