{
  "id": "1305.1827",
  "version": "v1",
  "published": "2013-05-08T14:25:33.000Z",
  "updated": "2013-05-08T14:25:33.000Z",
  "title": "Notes on the Krupa-Zawisza Ultrapower of Self-Adjoint Operators",
  "authors": [
    "Hiroshi Ando",
    "Izumi Ojima",
    "Hayato Saigo"
  ],
  "comment": "13pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "It is known that there is a difficulty in constructing the ultrapower of unbounded operators. Krupa and Zawisza gave a rigorous definition of the ultrapower A^{omega} of a selfadjoint operator A. In this note, we give alternative description of A^{omega} and the Hilbert space H(A) on which A^{omega} is densely defined, which provides a criterion to determine to which representing sequence (\\xi_n)n of a given vector \\xi in dom(A^{omega}) has the property that A^{omega}\\xi = (A\\xi_n)_{omega} holds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-08T14:25:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A10",
      "03C20"
    ],
    "keywords": [
      "self-adjoint operators",
      "krupa-zawisza ultrapower",
      "hilbert space",
      "selfadjoint operator",
      "zawisza gave"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.1827A"
    }
  }
}