{
  "id": "2402.04003",
  "version": "v1",
  "published": "2024-02-06T13:58:53.000Z",
  "updated": "2024-02-06T13:58:53.000Z",
  "title": "Generalized Cesàro operators in weighted Banach spaces of analytic functions with sup-norms",
  "authors": [
    "Angela A. Albanese",
    "José Bonet",
    "Werner J. Ricker"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "An investigation is made of the generalized Ces\\`aro operators $C_t$, for $t\\in [0,1]$, when they act on the space $H(\\mathbb{D})$ of holomorphic functions on the open unit disc $\\mathbb{D}$, on the Banach space $H^\\infty$ of bounded analytic functions and on the weighted Banach spaces $H_v^\\infty$ and $H_v^0$ with their sup-norms. Of particular interest are the continuity, compactness, spectrum and point spectrum of $C_t$ as well as their linear dynamics and mean ergodicity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-06T13:58:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E15",
      "47B38",
      "46E10",
      "47A10",
      "47A16",
      "47A35"
    ],
    "keywords": [
      "weighted banach spaces",
      "generalized cesàro operators",
      "open unit disc",
      "bounded analytic functions",
      "holomorphic functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}