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

The source file(s), kaltonlancienarxiv.tex: 58313 bytes, is(are) stored in gzipped form as 0708.3924.gz with size 16kb. The corresponding postcript file has gzipped size 122kb.

Submitted from: gilles.lancien@univ-fcomte.fr

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