{
  "id": "math/0610421",
  "version": "v1",
  "published": "2006-10-12T22:40:40.000Z",
  "updated": "2006-10-12T22:40:40.000Z",
  "title": "Smooth norms and approximation in Banach spaces of the type C(K)",
  "authors": [
    "Petr Hajek",
    "Richard Haydon"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove two theorems about differentiable functions on the Banach space C(K), where K is compact. (i) If C(K) admits a non-trivial function of class C^m and of bounded support, then all continuous real-valued functions on C(K) may be uniformly approximated by functions of class C^m. (ii) If C(K) admits an equivalent norm with locally uniformly convex dual norm, then C(K) admits an equivalent norm which is of class C^infty (except at 0).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-12T22:40:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B03",
      "46B26"
    ],
    "keywords": [
      "banach space",
      "smooth norms",
      "approximation",
      "equivalent norm",
      "locally uniformly convex dual norm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10421H"
    }
  }
}