On ϕ ⊗ ψ-Strongly Connes Amenability for Certain Dual Banach Algebras

چکیده مقاله

Abstract. In this paper, the notions of strongly Connes amenability for explicit products of Banach algebras and module extension of a Banach algebra is developed. Indeed, we characterize ϕ -strongly Connes amenability of projective tensor product Ab B via so-called ϕ -wc virtual diagonals and as a result ϕ -normal virtual diagonals, where ϕ 2 A and 2 B, are two-linear functionals on dual Banach algebras A and B, respectively. Also, we present necessary and sufficient conditions for the existence of (ϕ; )-wc virtual diagonals in -Lau product A B. Finally, we characterize (ϕ; 0)-wc virtual diagonal and (ϕ; 0)-strongly Connes amenability for the module extension of Banach algebra A X, where X is a normal Banach A-bimodule with predual X.