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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access July 1, 2015

Tight Embeddability of Proper and Stable Metric Spaces

  • F. Baudier and G. Lancien


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 ℓpn’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.

MSC: 46B85; 46B20


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Received: 2015-3-20
Accepted: 2015-5-27
Published Online: 2015-7-1

© 2015 F. Baudier, G. Lancien

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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