Johnson pseudo-contractibility and pseudo-amenability of $ θ$-Lau product of Banach algebras

Abstract

Given Banach algebras A and B with θ ∈ ∆(B). We shall study the Johnson pseudocontractibility and pseudo-amenability of θ-Lau product A × θ B. We show that if A × θ B is Johnson pseudo-contractible, then A is Johnson pseudo-contractible and has a bounded approximate identity and B is Johnson pseudo-contractible. In some particular cases complete characterization of Johnson pseudocontractibility of A × θ B are given. Also, we show that pseudo-amenability of A × θ B implies approximate amenability of A and pseudo-amenability of B.[19] A. Sahami and A. Pourabbas, Johnson pseudo-contractibility of certain semigroup algebras, Semigroup Forum (2017).