{
  "id": "2302.12547",
  "version": "v1",
  "published": "2023-02-24T10:01:36.000Z",
  "updated": "2023-02-24T10:01:36.000Z",
  "title": "Composition operators and convexity of their Berezin range",
  "authors": [
    "Athul Augustine",
    "P. Shankar"
  ],
  "comment": "16 pages, 9 figures",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "Berezin range of a bounded operator $T$ acting on a reproducing kernel Hilbert space $\\mathcal{H}$ is the set $B(T)$ := $\\{\\langle T\\hat{k}_{x},\\hat{k}_{x} \\rangle_{\\mathcal{H}} : x \\in X\\}$, where $\\hat{k}_{x}$ is the normalized reproducing kernel for $\\mathcal{H}$ at $x \\in X$. In general, the Berezin range of an operator is not convex. In this paper, we discuss the convexity of range of the Berezin transforms. We characterize the convexity of the Berezin range for a class of composition operators acting on Hardy space and Bergman space of the unit disk.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-24T10:01:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B32",
      "52A10"
    ],
    "keywords": [
      "berezin range",
      "composition operators",
      "reproducing kernel hilbert space",
      "berezin transforms",
      "unit disk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}