{
  "id": "math/9701203",
  "version": "v1",
  "published": "1997-01-17T00:00:00.000Z",
  "updated": "1997-01-17T00:00:00.000Z",
  "title": "Banach spaces determined by their uniform structures",
  "authors": [
    "William B. Johnson",
    "Joram Lindenstrauss",
    "Gideon Schechtman"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Following results of Bourgain and Gorelik we show that the spaces $\\ell_p$, $1<p<\\infty$, as well as some related spaces have the following uniqueness property: If $X$ is a Banach space uniformly homeomorphic to one of these spaces then it is linearly isomorphic to the same space. We also prove that if a $C(K)$ space is uniformly homeomorphic to $c_0$, then it is isomorphic to $c_0$. We show also that there are Banach spaces which are uniformly homeomorphic to exactly $2$ isomorphically distinct spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-01-17T00:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20"
    ],
    "keywords": [
      "banach spaces",
      "uniform structures",
      "banach space uniformly homeomorphic",
      "uniqueness property",
      "isomorphically distinct spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1997math......1203J"
    }
  }
}