{
  "id": "1510.07289",
  "version": "v1",
  "published": "2015-10-25T19:06:21.000Z",
  "updated": "2015-10-25T19:06:21.000Z",
  "title": "On Dvoretzky's theorem for subspaces of $L_p$",
  "authors": [
    "Grigoris Paouris",
    "Petros Valettas"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "We prove that for any $p > 2$ and every $n$-dimensional subspace $X$ of $L_p$, the Euclidean space $\\ell_2^k$ can be $(1 + \\varepsilon)$-embedded into $X$ with $k \\geq c_p \\min\\{\\varepsilon^2 n, (\\varepsilon n)^{2/p} \\}$, where $c_p > 0$ is a constant depending only on $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-25T19:06:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B07",
      "46B09"
    ],
    "keywords": [
      "dvoretzkys theorem",
      "dimensional subspace"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151007289P"
    }
  }
}