{
  "id": "2311.15245",
  "version": "v1",
  "published": "2023-11-26T09:16:22.000Z",
  "updated": "2023-11-26T09:16:22.000Z",
  "title": "The Cesaro Operator in $\\ell^{2}$ is Essentially Normal",
  "authors": [
    "Uğur Gül"
  ],
  "comment": "6 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we prove that the Cesaro operator $\\mathcal{C}$ in $\\ell^{2}$, the Hilbert space of square summable sequences, is essentially normal, i.e. the commutator $[\\mathcal{C}^{\\ast},\\mathcal{C}]:=\\mathcal{C}^{\\ast}\\mathcal{C}-\\mathcal{C}\\mathcal{C}^{\\ast}$ is a compact operator on $\\ell^{2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-26T09:16:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cesaro operator",
      "essentially normal",
      "square summable sequences",
      "compact operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}