Generalization of the weak amenability on various Banach algebras

Abstract

The generalized notion of weak amenability, namely (ϕ, ψ)-weak amenability, where ϕ, ψ are continuous homomorphisms on a Banach algebra A, was introduced by Bodaghi, Eshaghi Gordji and Medghalchi (2009). In this paper, the (ϕ, ψ)-weak amenability on the measure algebra M (G), the group algebra L 1 (G) and the Segal algebra S 1 (G), where G is a locally compact group, are studied. As a typical example, the (ϕ, ψ)-weak amenability of a special semigroup algebra is shown as well.