{
  "id": "1712.07075",
  "version": "v1",
  "published": "2017-12-19T17:43:27.000Z",
  "updated": "2017-12-19T17:43:27.000Z",
  "title": "Some sufficient conditions for existence of hyperinvariant subspaces for operators intertwined with unitaries",
  "authors": [
    "Maria F. Gamal'"
  ],
  "comment": "Submitted to Studia Math",
  "categories": [
    "math.FA"
  ],
  "abstract": "For a power bounded or polynomially bounded operator $T$ sufficient conditions for the existence of a nontrivial hyperinvariant subspace are given. The obtained hyperinvariant subspaces of $T$ have the form of the closure of the range of $\\varphi(T)$. Here $\\varphi$ is a singular inner function, if $T$ is polynomially bounded, or $\\varphi$ is an analytic in the unit disc function with absolutely summable Taylor coefficients and singular inner part, if $T$ is supposed to be power bounded only. Also, an example of a quasianalytic contraction $T$ is given. The quasianalytic spectral set of $T$ is not the whole unit circle $\\mathbb T$, while $\\sigma(T)=\\mathbb T$. Proofs are based on results by Esterle, Kellay, Borichev and Volberg.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-19T17:43:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A15",
      "47A60",
      "47A10"
    ],
    "keywords": [
      "sufficient conditions",
      "singular inner function",
      "nontrivial hyperinvariant subspace",
      "unit disc function",
      "singular inner part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}