Approximate biflatness and Johnson pseudo-contractibility of some Banach algebras

2018/06/11 by Amir Sahami, Sahami, Amir
Computer Science · Mathematics · #46H05 #46H20 #46M10 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis #math.FA #msc:46H05 #msc:46H20 #msc:46M10

paper · pdf · doi:10.48550/arxiv.1806.04198

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openalex publication_date 2018/06/11 · arxiv created 2018/08/30 · arxiv updated 2018/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a compact metric space X, the Lipschitz algebras Lip_α(X) and ℓ ip_α(X) are approximately biflat if and only if X is finite, provided that 0<α<1. We give an enough and sufficient condition that a vector-valued Lipschitz algebras is Johnson pseudo-contractible for each α>0. We also show that some triangular Banach algebras are not approximately biflat.

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