Tight Embeddability of Proper and Stable Metric Spaces

• Autorzy: F. Baudier , G. Lancien
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 46B85: Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-03-20

zaakceptowano

2015-05-27

online

2015-07-01

Twórcy

autor

F. Baudier

• 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

autor

G. Lancien

• Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cédex, France

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Identyfikatory

DOI

10.1515/agms-2015-0010