Characterization of module Connes amenability for certain Banach algebras by homomorphisms

چکیده مقاله

Let A=(A∗)∗ and B=(B∗)∗ be dual Banach algebras and U be a Banach algebra. Let also Ω=(Ω∗)∗ be a normal Banach A-bimodule and Π:B→A be an U-bimodule algebraic homomorphism. In this article, we investigate the notion of U-bimodule Connes amenability for the projective tensor product Aˆ⊗B pertinent to its closed two-sided ideals. Moreover, we characterize the U-bimodule (ψBU,θ)-Connes amenability of Π-Lau product A×ΠB, where ψAU:A→A is a w∗-continuous U-bimodule algebraic homomorphism, θ:B→C is a bounded linear functional such that θ∈B∗ (the predual of B) and A is Banach U-bimodule. Furthermore, we obtain a characterization for U-bimodule (ψBU,0)-Connes amenability of U-bimodule extension of Banach algebra A⊕Ω. Lastly, for more clarity of our results, we present some concrete examples in the setting of matrices algebra.