Tight Embeddability of Proper and Stable Metric Spaces
Résumé
We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for p ∈ [1, ∞], every proper subset of Lp is almost Lipschitzly embeddable into a Banach space X if and only if X contains uniformly the n p '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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