{
  "id": "1407.7160",
  "version": "v1",
  "published": "2014-07-26T21:14:02.000Z",
  "updated": "2014-07-26T21:14:02.000Z",
  "title": "On extensions of $J$-skew-symmetric and $J$-isometric operators",
  "authors": [
    "Sergey M. Zagorodnyuk"
  ],
  "comment": "5 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper it is proved that each densely defined $J$-skew-symmetric operator (or each $J$-isometric operator with $\\overline{D(A)}=\\overline{R(A)}=H$) in a Hilbert space $H$ has a $J$-skew-self-adjoint (respectively $J$-unitary) extension in a Hilbert space $\\widetilde H\\supseteq H$. We follow the ideas of Galindo in~[A.~Galindo, On the existence of $J$-self-adjoint extensions of $J$-symmetric operators with adjoint, Communications on pure and applied mathematics, Vol. XV, 423-425 (1962)] with necessary modifications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-26T21:14:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A20"
    ],
    "keywords": [
      "isometric operator",
      "hilbert space",
      "skew-symmetric operator",
      "necessary modifications",
      "self-adjoint extensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.7160Z"
    }
  }
}