{
  "id": "1707.04726",
  "version": "v1",
  "published": "2017-07-15T11:19:27.000Z",
  "updated": "2017-07-15T11:19:27.000Z",
  "title": "The Cesàro operator in weighted $\\ell_1$ spaces",
  "authors": [
    "Angela A. Albanese",
    "José Bonet",
    "Werner J. Ricker"
  ],
  "doi": "10.1002/mana.201600509",
  "categories": [
    "math.FA"
  ],
  "abstract": "Unlike for $\\ell_p$, $1<p\\leq\\infty$, the discrete Ces\\`aro operator $C$ does not map $\\ell_1$ into itself. We identify precisely those weights $w$ such that $C$ does map $\\ell_1(w)$ continuously into itself. For these weights a complete description of the eigenvalues and the spectrum of $C$ are presented. It is also possible to identify all $w$ such that $C$ is a compact operator in $\\ell_1(w)$. The final section investigates the mean ergodic properties of $C$ in $\\ell_1(w)$. Many examples are presented in order to supplement the results and to illustrate the phenomena that occur.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-15T11:19:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A10",
      "47B37",
      "46B45",
      "47A16",
      "47A35",
      "47B07"
    ],
    "keywords": [
      "cesàro operator",
      "mean ergodic properties",
      "final section",
      "complete description",
      "compact operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}