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arXiv · 1503.06089

Tight embeddability of proper and stable metric spaces

Florent Baudier·Gilles Lancien
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Abstract

We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for $p\in [1,\infty]$, every proper subset of $L_p$ is almost Lipschitzly embeddable into a Banach space $X$ if and only if $X$ contains uniformly the $\ell_p^n$'s. We also sharpen a result of N. Kalton by showing that every stable metric space is nearly isometrically embeddable in the class of reflexive Banach spaces.

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Florent Baudier, Gilles Lancien. 2015-03-20. Tight embeddability of proper and stable metric spaces. https://doi.org/10.1515/agms-2015-0010

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