{
  "id": "math/0007049",
  "version": "v3",
  "published": "2000-07-09T17:39:55.000Z",
  "updated": "2001-05-25T22:25:48.000Z",
  "title": "Commutativity up to a factor of bounded operators in complex Hilbert space",
  "authors": [
    "J. A. Brooke",
    "P. Busch",
    "D. B. Pearson"
  ],
  "comment": "9 pages. Material reorganised, new examples added to highlight relations between main results. Submitted to Proc. Roy. Soc. A",
  "journal": "Proc. Roy. Soc. A (London) 458 (2002) 109-118.",
  "doi": "10.1098/rspa.2001.0858",
  "categories": [
    "math.FA",
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "We explore commutativity up to a factor, $AB=\\lambda BA$, for bounded operators in a complex Hilbert space. Conditions on the possible values of the factor $\\lambda$ are formulated and shown to depend on spectral properties of the operators involved. Commutativity up to a unitary factor is considered for pairs of self-adjoint operators. Examples of nontrivial realizations of such commutation relations are given.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2001-05-25T22:25:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46N50",
      "47A05",
      "81P15"
    ],
    "keywords": [
      "complex hilbert space",
      "bounded operators",
      "commutativity",
      "spectral properties",
      "unitary factor"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Proceedings of the Royal Society of London Series A",
      "year": 2002,
      "month": "Jan",
      "volume": 458,
      "number": 2017,
      "pages": 109
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002RSPSA.458..109B"
    }
  }
}