{
  "id": "2306.02745",
  "version": "v1",
  "published": "2023-06-05T09:56:08.000Z",
  "updated": "2023-06-05T09:56:08.000Z",
  "title": "Convergence of operators with deficiency indices $(k,k)$ and of their self-adjoint extensions",
  "authors": [
    "August Bjerg"
  ],
  "comment": "12 pages, 0 figures",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We consider an abstract sequence $\\{A_n\\}_{n=1}^\\infty$ of closed symmetric operators on a separable Hilbert space $\\mathcal{H}$. It is assumed that all $A_n$'s have equal deficiency indices $(k,k)$ and thus self adjoint extensions $\\{B_n\\}_{n=1}^\\infty$ exist and are parametrized by partial isometries $\\{U_n\\}_{n=1}^\\infty$ on $\\mathcal{H}$ according to von Neumann's extension theory. Under two different convergence assumptions on the $A_n$'s we give the precise connection between strong resolvent convergence of the $B_n$'s and strong convergence of the $U_n$'s.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-05T09:56:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B25",
      "47B93",
      "81Q10"
    ],
    "keywords": [
      "self-adjoint extensions",
      "von neumanns extension theory",
      "strong resolvent convergence",
      "equal deficiency indices",
      "self adjoint extensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}