{
  "id": "2103.09266",
  "version": "v1",
  "published": "2021-03-16T18:21:16.000Z",
  "updated": "2021-03-16T18:21:16.000Z",
  "title": "Every non-smooth $2$-dimensional Banach space has the Mazur-Ulam property",
  "authors": [
    "Taras Banakh",
    "Javier Cabello Sánchez"
  ],
  "comment": "13 pages",
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "A Banach space $X$ has the $Mazur$-$Ulam$ $property$ if any isometry from the unit sphere of $X$ onto the unit sphere of any other Banach space $Y$ extends to a linear isometry of the Banach spaces $X,Y$. A Banach space $X$ is called $smooth$ if the unit ball has a unique supporting functional at each point of the unit sphere. We prove that each non-smooth 2-dimensional Banach space has the Mazur-Ulam property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-16T18:21:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B04",
      "46B20",
      "52A21",
      "52A10",
      "53A04",
      "54E35",
      "54E40"
    ],
    "keywords": [
      "dimensional banach space",
      "mazur-ulam property",
      "unit sphere",
      "non-smooth",
      "unit ball"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}