On the expansiveness of coarse maps between Banach spaces and geometry preservation

2023/10/09 by Bruno de Mendonça Braga, Gilles Lancien, Braga, Bruno de Mendonça +1
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2310.05684

openalex publication_date 2023/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new notion of embeddability between Banach spaces. By studying the classical Mazur map, we show that it is strictly weaker than the notion of coarse embeddability. We use the techniques from metric cotype introduced by M. Mendel and A. Naor to prove results about cotype preservation and complete our study of embeddability between ℓ_p spaces. We confront our notion with nonlinear invariants introduced by N. Kalton, which are defined in terms of concentration properties for Lipschitz maps defined on countably branching Hamming or interlaced graphs. Finally, we address the problem of the embeddability into ℓ_∞.

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