Tight embeddability of proper and stable metric spaces

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.

19 pages

Cited by in corpus (1)

• The coarse geometry of Tsirelson's space and applications