{
  "id": "0904.0462",
  "version": "v2",
  "published": "2009-04-02T20:23:18.000Z",
  "updated": "2010-05-14T15:20:24.000Z",
  "title": "The universality of $\\ell_1$ as a dual space",
  "authors": [
    "Daniel Freeman",
    "Edward Odell",
    "Thomas Schlumprecht"
  ],
  "comment": "30 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $X$ be a Banach space with a separable dual. We prove that $X$ embeds isomorphically into a $\\cL_\\infty$ space $Z$ whose dual is isomorphic to $\\ell_1$. If, moreover, $U$ is a space so that $U$ and $X$ are totally incomparable, then we construct such a $Z$, so that $Z$ and $U$ are totally incomparable. If $X$ is separable and reflexive, we show that $Z$ can be made to be somewhat reflexive.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-05-14T15:20:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20"
    ],
    "keywords": [
      "dual space",
      "universality",
      "banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.0462F"
    }
  }
}