{
  "id": "2112.08813",
  "version": "v2",
  "published": "2021-12-16T11:58:23.000Z",
  "updated": "2022-12-06T23:33:01.000Z",
  "title": "Point spectrum and hypercyclicity problem for a class of truncated Toeplitz operators",
  "authors": [
    "Anton Baranov",
    "Andrei Lishanskii"
  ],
  "comment": "13 pages. Section 3 is substantially expanded",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "In this note we discuss an open problem whether a truncated Toeplitz operator on a model space can be hypercyclic. We compute point spectrum and eigenfunctions for a class of truncated Toeplitz operators with polynomial analytic and antianalytic parts. We show that, for a class of model spaces, truncated Toeplitz operators with symbols of the form $\\Phi(z) =a \\bar{z} +b + cz$, $|a| \\ne |c|$, have complete sets of eigenvectors, and, in particular, are not hypercyclic.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-12-06T23:33:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A16",
      "47B35",
      "30H10"
    ],
    "keywords": [
      "truncated toeplitz operator",
      "point spectrum",
      "hypercyclicity problem",
      "model space",
      "open problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}