{
  "id": "0708.3924",
  "version": "v1",
  "published": "2007-08-29T10:08:13.000Z",
  "updated": "2007-08-29T10:08:13.000Z",
  "title": "Best constants for Lipschitz embeddings of metric spaces into c_0",
  "authors": [
    "N. J. Kalton",
    "G. Lancien"
  ],
  "comment": "22 pages",
  "categories": [
    "math.FA"
  ],
  "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 $c_0^+$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-29T10:08:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46T99"
    ],
    "keywords": [
      "best constant",
      "banach space embeds",
      "study lipschitz embeddings",
      "separable metric space",
      "earlier estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.3924K"
    }
  }
}