{
  "id": "0807.3835",
  "version": "v1",
  "published": "2008-07-24T09:52:50.000Z",
  "updated": "2008-07-24T09:52:50.000Z",
  "title": "Biseparating maps between Lipschitz function spaces",
  "authors": [
    "Jesus Araujo",
    "Luis Dubarbie"
  ],
  "comment": "17 pages; no figures",
  "categories": [
    "math.FA"
  ],
  "abstract": "For complete metric spaces $X$ and $Y$, a description of linear biseparating maps between spaces of vector-valued Lipschitz functions defined on $X$ and $Y$ is provided. In particular it is proved that $X$ and $Y$ are bi-Lipschitz homeomorphic, and the automatic continuity of such maps is derived in some cases. Besides, these results are used to characterize the separating bijections between scalar-valued Lipschitz function spaces when $Y$ is compact.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-07-24T09:52:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B38",
      "46E40",
      "46H40",
      "47B33"
    ],
    "keywords": [
      "complete metric spaces",
      "scalar-valued lipschitz function spaces",
      "linear biseparating maps",
      "bi-lipschitz homeomorphic",
      "automatic continuity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.3835A"
    }
  }
}