{
  "id": "1704.02251",
  "version": "v1",
  "published": "2017-04-07T14:46:54.000Z",
  "updated": "2017-04-07T14:46:54.000Z",
  "title": "The Cesàro operator on power series spaces",
  "authors": [
    "Angela A. Albanese",
    "José Bonet",
    "Werner J. Ricker"
  ],
  "comment": "This article is accepted for publication in Studia Math",
  "categories": [
    "math.FA"
  ],
  "abstract": "The discrete Ces\\`aro operator $\\mathsf{C}$ is investigated in the class of power series spaces $\\Lambda_0(\\alpha)$ of finite type. Of main interest is its spectrum, which is distinctly different when the underlying Fr\\'echet space $\\Lambda_0(\\alpha)$ is nuclear as for the case when it is not. Actually, the nuclearity of $\\Lambda_0(\\alpha)$ is characterized via certain properties of the spectrum of $\\mathsf{C}$. Moreover, $\\mathsf{C}$ is always power bounded, uniformly mean ergodic and, whenever $\\Lambda_0(\\alpha)$ is nuclear, also has the property that the range $(I-\\mathsf{C})^m(\\Lambda_0(\\alpha))$ is closed in $\\Lambda_0(\\alpha)$, for each $m\\in\\mathbb{N}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-07T14:46:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A10",
      "47A35",
      "47B37",
      "46A04",
      "47A16",
      "46A45",
      "46B45"
    ],
    "keywords": [
      "power series spaces",
      "cesàro operator",
      "finite type",
      "frechet space",
      "uniformly mean ergodic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}