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

2018/01/07 by M. Askari-Sayah, Askari-Sayah, M., A. Pourabbas +3
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.1801.02208

Abstract

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 .

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