{
  "id": "2002.02344",
  "version": "v1",
  "published": "2020-02-06T16:44:06.000Z",
  "updated": "2020-02-06T16:44:06.000Z",
  "title": "Essential Commutants and Characterizations of the Toeplitz Algebra",
  "authors": [
    "Raffael Hagger"
  ],
  "comment": "17 pages",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "In this paper we study the Toeplitz algebra, which is generated by Toeplitz operators with bounded symbols on the Fock space $F^p_{\\alpha}$. We show that the Toeplitz algebra coincides with each of the algebras generated by band-dominated, sufficiently localized and weakly localized operators, respectively. Moreover, we determine its essential commutant and its essential bicommutant. For $p = 2$ these results were obtained recently by Xia. However, Xia's ideas are mostly connected to Hilbert space theory and methods which are not applicable for $p \\neq 2$. Instead, we use a recent result of Fulsche to generalize Xia's theorems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-06T16:44:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B35",
      "30H20",
      "47L10",
      "47L80"
    ],
    "keywords": [
      "essential commutant",
      "characterizations",
      "toeplitz algebra coincides",
      "hilbert space theory",
      "essential bicommutant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}