Hamming graphs and concentration properties in non-quasi-reflexive Banach spaces

2021/06/08 by Audrey Fovelle, Fovelle, Audrey
Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2106.04297

openalex publication_date 2021/06/08 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In this note, we study some concentration properties for Lipschitz maps defined on Hamming graphs, as well as their stability under sums of Banach spaces. As an application, we extend a result of Causey on the coarse Lipschitz structure of quasi-reflexive spaces satisfying upper ℓ_p tree estimates to the setting of ℓ_p-sums of such spaces. Our result provides us with a tool for constructing the first examples of Banach spaces that are not quasi-reflexive but nevertheless admit some concentration inequality. We also give a sufficient condition for a space to be asymptotic-c₀ in terms of a concentration property, as well as relevant counterexamples.

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