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arXiv · 1801.02208

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

M. Askari-Sayah·A. Pourabbas·A. Sahami
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Abstract

Given Banach algebras $ A $ and $ B $ with $ \theta\in\Delta(B) $. We shall study the Johnson pseudo-contractibility and pseudo-amenability of $ \theta $-Lau product $ A\times_{\theta} B $. We show that if $ A\times_{\theta} 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\times_{\theta} B $ are given. Also, we show that pseudo-amenability of $ A\times_{\theta} B $ implies approximate amenability of $ A $ and pseudo-amenability of $ B $.

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M. Askari-Sayah, A. Pourabbas, A. Sahami. 2018-01-07. Johnson pseudo-contractibility and pseudo-amenability of $ \theta $-Lau product of Banach algebras. https://arxiv.org/abs/1801.02208

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