Abstract

In this paper, the notions of strong Connes amenability for certain products of Banach algebras and module extension of dual Banach algebras is investigated. We characterize χ ⊗ η-strong Connes amenability of projective tensor product K⨶H via χ ⊗ η-σwc virtual diagonals, where χ ∈ K∗ and η ∈ H∗ are linear functionals on dual Banach algebras K and H, respectively. Also, we present some conditions for the existence of (χ, θ)-σwc virtual diagonals in the θ-Lau product of K ×_θ H. Finally, we characterize the notion of (χ, 0)-strong Connes amenability for module extension of dual Banach algebras K ⊕ X, where X is a normal Banach K-bimodule.