{
  "id": "1812.07239",
  "version": "v1",
  "published": "2018-12-18T08:49:45.000Z",
  "updated": "2018-12-18T08:49:45.000Z",
  "title": "A Toeplitz-like operator with rational symbol having poles on the unit circle III: the adjoint",
  "authors": [
    "G. J. Groenewald",
    "S. Ter Horst",
    "J. Jaftha",
    "A. C. M. Ran"
  ],
  "comment": "19 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "This paper contains a further analysis of the Toeplitz-like operators $T_\\omega$ on $H^p$ with rational symbol $\\omega$ having poles on the unit circle that were previously studied in [5.6]. Here the adjoint operator $T_\\omega^*$ is described. In the case where $p=2$ and $\\omega$ has poles only on the unit circle $\\mathbb{T}$, a description is given for when $T_\\omega^*$ is symmetric and when $T_\\omega^*$ admits a selfadjoint extension. Also in the case where $p=2$, $\\omega$ has only poles on $\\mathbb{T}$ and in addition $\\omega$ is proper, it is shown that $T_\\omega^*$ coincides with the unbounded Toeplitz operator defined by Sarason in [10].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-18T08:49:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B35",
      "47A53",
      "47A68"
    ],
    "keywords": [
      "unit circle",
      "rational symbol",
      "toeplitz-like operator",
      "paper contains",
      "unbounded toeplitz operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}