{
  "id": "1704.08984",
  "version": "v1",
  "published": "2017-04-28T15:41:22.000Z",
  "updated": "2017-04-28T15:41:22.000Z",
  "title": "Operators invariant relative to a completely nonunitary contraction",
  "authors": [
    "H. Bercovici",
    "D. Timotin"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Given a contraction A on a Hilbert space H, an operator T on H is said to be A-invariant if <Tx,x>=<TAx,Ax> for every x in H such that ||Ax||=||x||. In the special case in which both defect indices of A are equal to 1, we show that every A-invariant operator is the compression to H of an unbounded linear transformation that commutes with the minimal unitary dilation of A. This result was proved by Sarason under the additional hypothesis that A is of class C_{00}, leading to an intrinsic characterization of the truncated Toeplitz operators. We also adapt to our more general context other results about truncated Toeplitz operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-28T15:41:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A45",
      "47B35"
    ],
    "keywords": [
      "operators invariant relative",
      "nonunitary contraction",
      "truncated toeplitz operators",
      "minimal unitary dilation",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}