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Pré-Publication, Document De Travail Année : 2023

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

Résumé

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 $\ell_p$ 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 $\ell_\infty$.
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Dates et versions

hal-04240487 , version 1 (13-10-2023)

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  • HAL Id : hal-04240487 , version 1

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Gilles Lancien, Bruno de Mendonça Braga. On the expansiveness of coarse maps between Banach spaces and geometry preservation. 2023. ⟨hal-04240487⟩
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