1Department of Mathematics University of Missouri-Columbia Columbia, MO 65211, U.S.A. 2Laboratoire 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
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 $c_0^+$.
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
Affiliations des auteurs :
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
