Some properties of coarse Lipschitz maps between Banach spaces

2016/12/05 by Aude Dalet, Gilles Lancien, Dalet, Aude +1
Mathematics · #46B20 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Primary 46B80 #Secondary 46B03

paper · pdf · doi:10.48550/arxiv.1612.01364

openalex publication_date 2016/12/05 · openalex created_date 2016/12/16 · openalex updated_date 2026/07/28

Abstract

We study the structure of the space of coarse Lipschitz maps between Banach spaces. In particular we introduce the notion of norm attaining coarse Lipschitz maps. We extend to the case of norm attaining coarse Lipschitz equivalences, a result of G. Godefroy on Lipschitz equivalences. This leads us to include the non separable versions of classical results on the stability of the existence of asymptotically uniformly smooth norms under Lipschitz or coarse Lipschitz equivalences.

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