{
  "id": "0906.2989",
  "version": "v2",
  "published": "2009-06-16T18:04:27.000Z",
  "updated": "2010-01-28T09:39:05.000Z",
  "title": "Smooth extensions of functions on separable Banach spaces",
  "authors": [
    "D. Azagra",
    "R. Fry",
    "L. Keener"
  ],
  "comment": "19 pages. This version fixes a gap in the previous proof of Theorem 1 by providing a sharp version of Lemma 1",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $X$ be a Banach space with a separable dual $X^{*}$. Let $Y\\subset X$ be a closed subspace, and $f:Y\\to\\mathbb{R}$ a $C^{1}$-smooth function. Then we show there is a $C^{1}$ extension of $f$ to $X$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-01-28T09:39:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20"
    ],
    "keywords": [
      "separable banach spaces",
      "smooth extensions",
      "smooth function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.2989A"
    }
  }
}