{
  "id": "1812.10342",
  "version": "v1",
  "published": "2018-12-26T15:30:15.000Z",
  "updated": "2018-12-26T15:30:15.000Z",
  "title": "2-local maps, surjective isometries, continuously differentiable maps",
  "authors": [
    "Osamu Hatori",
    "Shiho Oi"
  ],
  "comment": "22 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study 2-local reflexivity of the set of all surjective isometries between certain function spaces. We do not assume linearity for isometries. We prove that a 2-local isometry in the group of all surjective isometries on the algebra of all continuously differentiable functions on the closed unit interval with respect to several norms is a surjective isometry. We also prove that a 2-local isometry in the group of all surjective isometries on the Banach algebra of all Lipschitz functions on the closed unit interval with the sum-norm is a surjective isometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-26T15:30:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B04",
      "46J15",
      "46J10"
    ],
    "keywords": [
      "surjective isometry",
      "continuously differentiable maps",
      "closed unit interval",
      "banach algebra",
      "assume linearity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}