{
  "id": "math/0405565",
  "version": "v1",
  "published": "2004-05-28T17:33:45.000Z",
  "updated": "2004-05-28T17:33:45.000Z",
  "title": "On the extension of Hölder maps with values in spaces of continuous functions",
  "authors": [
    "Gilles Lancien",
    "Beata Randrianantoanina"
  ],
  "comment": "16 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the isometric extension problem for H\\\"{o}lder maps from subsets of any Banach space into $c_0$ or into a space of continuous functions. For a Banach space $X$, we prove that any $\\alpha$-H\\\"{o}lder map, with $0<\\alpha\\leq 1$, from a subset of $X$ into $c_0$ can be isometrically extended to $X$ if and only if $X$ is finite dimensional. For a finite dimensional normed space $X$ and for a compact metric space $K$, we prove that the set of $\\alpha$'s for which all $\\alpha$-H\\\"{o}lder maps from a subset of $X$ into $C(K)$ can be extended isometrically is either $(0,1]$ or $(0,1)$ and we give examples of both occurrences. We also prove that for any metric space $X$, the described above set of $\\al$'s does not depend on $K$, but only on finiteness of $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-28T17:33:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46T99",
      "54C20",
      "54E35"
    ],
    "keywords": [
      "continuous functions",
      "hölder maps",
      "banach space",
      "compact metric space",
      "finite dimensional normed space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5565L"
    }
  }
}