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Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel


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2299-3274
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Tight Embeddability of Proper and Stable Metric Spaces

F. Baudier
  • Corresponding author
  • Institut de Mathématiques Jussieu-Paris Rive Gauche, Université Pierre et Marie Curie, Paris, France and Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ G. Lancien
  • Corresponding author
  • Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cédex, France
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-07-01 | DOI: https://doi.org/10.1515/agms-2015-0010

Abstract

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.

Keywords: almost Lipschitz embeddability; nearly isometric embeddability; proper metric spaces; stable metric spaces

MSC: 46B85; 46B20

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About the article

Received: 2015-03-20

Accepted: 2015-05-27

Published Online: 2015-07-01


Citation Information: Analysis and Geometry in Metric Spaces, Volume 3, Issue 1, ISSN (Online) 2299-3274, DOI: https://doi.org/10.1515/agms-2015-0010.

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© 2015 F. Baudier, G. Lancien. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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