{
  "id": "0810.3881",
  "version": "v1",
  "published": "2008-10-21T17:40:02.000Z",
  "updated": "2008-10-21T17:40:02.000Z",
  "title": "Corrigendum to \"Approximation by C^{p}-smooth, Lipschitz functions on Banach spaces\" [J. Math. Anal. Appl., 315 (2006), 599-605]",
  "authors": [
    "R. Fry"
  ],
  "journal": "Journal of Mathematical Analysis and Applications, Volume 348, Issue 1, 1 December 2008, Page 571",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this erratum, we recover the results from an earlier paper of the author's which contained a gap. Specifically, we prove that if X is a Banach space with an unconditional basis and admits a C^{p}-smooth, Lipschitz bump function, and Y is a convex subset of X, then any uniformly continuous function f: Y->R can be uniformly approximated by Lipschitz, C^{p}-smooth functions K:X->R. Also, if Z is any Banach space and f:X->Z is L-Lipschitz, then the approximates K:X->Z can be chosen CL-Lipschitz and C^{p}-smooth, for some constant C depending only on X.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-21T17:40:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20"
    ],
    "keywords": [
      "banach space",
      "lipschitz functions",
      "corrigendum",
      "approximation",
      "lipschitz bump function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jmaa.2008.08.007",
      "journal": "Journal of Mathematical Analysis and Applications",
      "year": 2008,
      "month": "Dec",
      "volume": 348,
      "number": 1,
      "pages": 571
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JMAA..348..571F"
    }
  }
}