MODULE CONNES AMENABILITY FOR PROJECTIVE TENSOR PRODUCT AND Θ-LAU PRODUT OF BANACH ALGEBRAS

Let A and B be Banach algebras with preduals A∗ and B∗ respectively, and Θ : B → A be an algebraic homomorphism. In this paper, we derive some specific results concerning the characterizations of module Connes amenability of certain Banach algebras. Indeed, we investigate and give necessary and sufficient conditions for module Connes amenability of projective tensor product A⊗B. Moreover, we characterize the module (ψ, θ)- Connes amenability of Θ-Lau product A×Θ B, which ψ and θ are homomorphisms in A∗ and B∗, respectively.