Geodesic
Best constants for Lipschitz embeddings of metric spaces into $c_0$
N. J. Kalton 1   ; G. Lancien 2
1 Department of Mathematics University of Missouri-Columbia Columbia, MO 65211, U.S.A.
2 Laboratoire de Mathématiques UMR 6623 Université de Franche-Comté 16 route de Gray 25030 Besançon Cedex, France
Fundamenta Mathematicae, Tome 199 (2008) no. 3, pp. 249-272 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We answer a question of Aharoni by showing that every separable metric space can be Lipschitz 2-embedded into $c_0$ 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 $\ell _p$-spaces into $c_0$ and give other applications. We prove that if a Banach space embeds almost isometrically into $c_0$, then it embeds linearly almost isometrically into $c_0$. We also study Lipschitz embeddings into $c_0^+$.
DOI : 10.4064/fm199-3-4
Keywords: answer question aharoni showing every separable metric space lipschitz embedded result sharp improves earlier estimates aharoni assouad pelant methods examine best constant lipschitz embeddings classical ell p spaces other applications prove banach space embeds almost isometrically embeds linearly almost isometrically study lipschitz embeddings

N. J. Kalton  1   ; G. Lancien  2

1 Department of Mathematics University of Missouri-Columbia Columbia, MO 65211, U.S.A.
2 Laboratoire de Mathématiques UMR 6623 Université de Franche-Comté 16 route de Gray 25030 Besançon Cedex, France 
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N. J. Kalton; G. Lancien. Best constants for Lipschitz embeddings of
 metric spaces into $c_0$. Fundamenta Mathematicae, Tome 199 (2008) no. 3, pp. 249-272. doi: 10.4064/fm199-3-4

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