{
  "id": "1903.11424",
  "version": "v1",
  "published": "2019-03-27T13:47:59.000Z",
  "updated": "2019-03-27T13:47:59.000Z",
  "title": "A generalization of the Kowalski -S\\{l} odkowski theorem and its application to 2-local maps on function spaces",
  "authors": [
    "Shiho Oi"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we extend a spherical variant of the Kowalski-S\\{l}odkowski theorem due to Li, Peralta, Wang and Wang \\cite{lpww}. As a corollary, we prove that every 2-local map in the set of all surjective isometries (without assuming linearity) on a certain function space is in fact a surjective isometry. This gives an affirmative answer to the problem on 2-local isometries posed by Moln\\'ar.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-27T13:47:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B04",
      "46B20",
      "46J10",
      "46J15",
      "30H05"
    ],
    "keywords": [
      "function space",
      "odkowski theorem",
      "generalization",
      "application",
      "surjective isometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}