{
  "id": "math/0209057",
  "version": "v1",
  "published": "2002-09-06T07:56:04.000Z",
  "updated": "2002-09-06T07:56:04.000Z",
  "title": "Orthogonality preserving transformations on indefinite inner product spaces: Generalization of Uhlhorn's version of Wigner's theorem",
  "authors": [
    "Lajos Molnar"
  ],
  "comment": "13 pages, To appear in J. Funct. Anal",
  "categories": [
    "math.FA",
    "quant-ph"
  ],
  "abstract": "We present an analogue of Uhlhorn's version of Wigner's theorem on symmetry transformations for the case of indefinite inner product spaces. This significantly generalizes a result of Van den Broek. The proof is based on our main theorem, which describes the form of all bijective transformations on the set of all rank-one idempotents of a Banach space which preserve zero products in both directions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-09-06T07:56:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "indefinite inner product spaces",
      "orthogonality preserving transformations",
      "uhlhorns version",
      "wigners theorem",
      "generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......9057M"
    }
  }
}