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Article Dans Une Revue Analysis and Geometry in Metric Spaces Année : 2015

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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Dates et versions

hal-01763771 , version 1 (11-04-2018)

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Gilles Lancien, F. Baudier. Tight Embeddability of Proper and Stable Metric Spaces. Analysis and Geometry in Metric Spaces, 2015, 3 (1), ⟨10.1515/agms-2015-0010⟩. ⟨hal-01763771⟩
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