{
  "id": "math/9212203",
  "version": "v1",
  "published": "1992-12-04T21:58:37.000Z",
  "updated": "1992-12-04T21:58:37.000Z",
  "title": "Operators preserving orthogonality are isometries",
  "authors": [
    "Alexander Koldobsky"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $E$ be a real Banach space. For $x,y \\in E,$ we follow R.James in saying that $x$ is orthogonal to $y$ if $\\|x+\\alpha y\\|\\geq \\|x\\|$ for every $\\alpha \\in R$. We prove that every operator from $E$ into itself preserving orthogonality is an isometry multiplied by a constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1992-12-04T21:58:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "operators preserving orthogonality",
      "real banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1992math.....12203K"
    }
  }
}