{
  "id": "0907.0241",
  "version": "v4",
  "published": "2009-07-01T20:58:18.000Z",
  "updated": "2009-11-24T16:25:47.000Z",
  "title": "Approximation of Lipschitz functions by Lipschitz, C^{p} smooth functions on weakly compactly generated Banach spaces",
  "authors": [
    "R. Fry",
    "L. Keener"
  ],
  "comment": "Added comments, a few corrections. 16 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "This note corrects a gap and improves results in an earlier paper by the first named author. More precisely, it is shown that on weakly compactly generated Banach spaces X which admit a C^{p} smooth norm, one can uniformly approximate uniformly continuous functions f:X->R by Lipschitz, C^{p} smooth functions. Moreover, there is a constant C>1 so that any L-Lipschitz function f:X->R can be uniformly approximated by CL-Lipschitz, C^{p} smooth functions. This provides a `Lipschitz version' of the classical approximation results of Godefroy, Troyanski, Whitfield and Zizler.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-11-24T16:25:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20"
    ],
    "keywords": [
      "weakly compactly generated banach spaces",
      "smooth functions",
      "lipschitz functions",
      "approximate uniformly continuous functions",
      "approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.0241F"
    }
  }
}