Asymptotic coarse Lipschitz equivalence

2023/02/23 by Bruno de Mendonça Braga, Gilles Lancien, Braga, Bruno de Mendonça +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2302.12016

Abstract

We introduce the notion of asymptotic coarse Lipschitz equivalence of metric spaces. We show that it is strictly weaker than coarse Lipschitz equivalence. We study its impact on the asymptotic dimension of metric spaces. Then we focus on Banach spaces. We prove that, for 2≤ p<∞, being linearly isomorphic to ℓ_p is stable under asymptotic coarse Lipschitz equivalences. Finally, we establish a version of the Gorelik principle in this setting and apply it to prove the stability of various properties of asymptotic uniform smoothness of Banach spaces under asymptotic coarse Lipschitz equivalences.

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