{
  "id": "1704.06961",
  "version": "v1",
  "published": "2017-04-23T18:54:40.000Z",
  "updated": "2017-04-23T18:54:40.000Z",
  "title": "Non-expansive bijections between unit balls of Banach spaces",
  "authors": [
    "Olesia Zavarzina"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "It is known that if $M$ is a finite-dimensional Banach space, or a strictly convex space, or the space $\\ell_1$, then every non-expansive bijection $F: B_M \\to B_M$ is an isometry. We extend these results to non-expansive bijections $F: B_E \\to B_M$ between unit balls of two different Banach spaces. Namely, if $E$ is an arbitrary Banach space and $M$ is finite-dimensional or strictly convex, or the space $\\ell_1$ then every non-expansive bijection $F: B_E \\to B_M$ is an isometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-23T18:54:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20"
    ],
    "keywords": [
      "non-expansive bijection",
      "unit balls",
      "finite-dimensional banach space",
      "arbitrary banach space",
      "strictly convex space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}