{
  "id": "math/9606209",
  "version": "v1",
  "published": "1996-06-05T00:00:00.000Z",
  "updated": "1996-06-05T00:00:00.000Z",
  "title": "Concerning the Bourgain $ell_1$ index of a Banach space",
  "authors": [
    "Robert Judd",
    "Edward Odell"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "A well known argument of James yields that if a Banach space $X$ contains $\\ell_1^n$'s uniformly then $X$ contains $\\ell_1^n$'s almost isometrically. In the first half of the paper we extend this idea to the ordinal $\\ell_1$-indices of Bourgain. In the second half we use our results to calculate the $\\ell_1$-index of certain Banach spaces. Furthermore we show that the $\\ell_1$-index of a separable Banach space not containing $\\ell_1$ must be of the form $\\omega^{\\alpha}$ for some countable ordinal $\\alpha$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1996-06-05T00:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20"
    ],
    "keywords": [
      "separable banach space",
      "second half",
      "james yields",
      "concerning",
      "first half"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1996math......6209J"
    }
  }
}