{
  "id": "1112.5888",
  "version": "v1",
  "published": "2011-12-26T19:51:34.000Z",
  "updated": "2011-12-26T19:51:34.000Z",
  "title": "On smooth extensions of vector-valued functions defined on closed subsets of Banach spaces",
  "authors": [
    "M. Jimenez-Sevilla",
    "L. Sanchez-Gonzalez"
  ],
  "comment": "17 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $X$ and $Z$ be Banach spaces, $A$ a closed subset of $X$ and a mapping $f:A \\to Z$. We give necessary and sufficient conditions to obtain a $C^1$ smooth mapping $F:X \\to Z$ such that $F_{\\mid_A}=f$, when either (i) $X$ and $Z$ are Hilbert spaces and $X$ is separable, or (ii) $X^*$ is separable and $Z$ is an absolute Lipschitz retract, or (iii) $X=L_2$ and $Z=L_p$ with $1<p<2$, or (iv) $X=L_p$ and $Z=L_2$ with $2<p<\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-26T19:51:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20"
    ],
    "keywords": [
      "banach spaces",
      "closed subset",
      "vector-valued functions",
      "smooth extensions",
      "absolute lipschitz retract"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.5888J"
    }
  }
}