Best constants for Lipschitz embeddings of metric spaces into c₀

• Autorzy: N. J. Kalton , G. Lancien
• Języki publikacji: EN

Abstrakty

EN

We answer a question of Aharoni by showing that every separable metric space can be Lipschitz 2-embedded into c₀ and this result is sharp; this improves earlier estimates of Aharoni, Assouad and Pelant. We use our methods to examine the best constant for Lipschitz embeddings of the classical $ℓ_p$-spaces into c₀ and give other applications. We prove that if a Banach space embeds almost isometrically into c₀, then it embeds linearly almost isometrically into c₀. We also study Lipschitz embeddings into c₀⁺.

Kategorie tematyczne

• 46T99: None of the above, but in this section
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 199
• Numer: 3
• Strony: 249-272

Daty

wydano

2008

Twórcy

autor

N. J. Kalton

• Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, U.S.A.

autor

G. Lancien

• Laboratoire de Mathématiques UMR 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France

Identyfikatory

DOI

10.4064/fm199-3-4