This is an announcement for the paper "Best constants for Lipschitz embeddings of metric spaces into $c_0$" by N.J. Kalton and G. Lancien.
Abstract: 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 $c_0^+$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20; 46T99
Remarks: 22 pages
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Submitted from: gilles.lancien@univ-fcomte.fr
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