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

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Given Banach algebras A and B with θ∈Δ(B). We shall study the Johnson pseudo-contractibility 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 pseudo-contractibility 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.