{
  "id": "1609.00812",
  "version": "v1",
  "published": "2016-09-03T10:21:39.000Z",
  "updated": "2016-09-03T10:21:39.000Z",
  "title": "The Cesaro operator in growth Banach spaces of analytic functions",
  "authors": [
    "Angela A. Albanese",
    "José Bonet",
    "Werner J. Ricker"
  ],
  "comment": "17 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "The Cesaro operator $\\mathsf{C}$, when acting in the classical growth Banach spaces $A^{-\\gamma}$ and $A_0^{-\\gamma}$, for $\\gamma > 0 $, of analytic functions on $\\mathbb{D}$, is investigated. Based on a detailed knowledge of their spectra (due to A. Aleman and A.-M. Persson) we are able to determine the norms of these operators precisely. It is then possible to characterize the mean ergodic and related properties of $\\mathsf{C}$ acting in these spaces. In addition, we determine the largest Banach space of analytic functions on $\\mathbb{D}$ which $\\mathsf{C}$ maps into $A^{-\\gamma}$ (resp. into $A_0^{-\\gamma}$); this optimal domain space always contains $A^{-\\gamma}$ (resp. $A_0^{-\\gamma}$) as a proper subspace.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-03T10:21:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B38",
      "46E15",
      "47A10",
      "47A16",
      "47A35"
    ],
    "keywords": [
      "analytic functions",
      "cesaro operator",
      "classical growth banach spaces",
      "optimal domain space",
      "largest banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}