Work

Asymptotic coarse Lipschitz equivalence

Year: 2026

Type: article

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.

Source: Annales de l’institut Fourier

DOI: 10.5802/aif.3775

Authors: Bruno M. Braga, Gilles Lancien

Institutions: Instituto Nacional de Matemática Pura e Aplicada, Centre National de la Recherche Scientifique, Laboratoire de Mathématiques de Besançon, Université Marie et Louis Pasteur

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Award: Large Scale Geometry in Functional Analysis