{
  "id": "1309.0164",
  "version": "v3",
  "published": "2013-08-31T22:45:15.000Z",
  "updated": "2014-07-14T08:32:24.000Z",
  "title": "Continuous and holomorphic functions with values in closed operators",
  "authors": [
    "Jan Dereziński",
    "Michał Wrochna"
  ],
  "comment": "final version, introduction reworked, 25 p",
  "categories": [
    "math.FA",
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We systematically derive general properties of continuous and holomorphic functions with values in closed operators, allowing in particular for operators with empty resolvent set. We provide criteria for a given operator-valued function to be continuous or holomorphic. This includes sufficient conditions for the sum and product of operator-valued holomorphic functions to be holomorphic. Using graphs of operators, operator-valued functions are identified with functions with values in subspaces of a Banach space. A special role is thus played by projections onto closed subspaces of a Banach space, which depend holomorphically on a parameter.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-14T08:32:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "closed operators",
      "continuous",
      "banach space",
      "operator-valued function",
      "empty resolvent set"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.4891759",
      "journal": "Journal of Mathematical Physics",
      "year": 2014,
      "month": "Aug",
      "volume": 55,
      "number": 8,
      "pages": "083512"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014JMP....55h3512D"
    }
  }
}