{
  "id": "0705.0970",
  "version": "v1",
  "published": "2007-05-07T19:38:13.000Z",
  "updated": "2007-05-07T19:38:13.000Z",
  "title": "On a Class of Ideals of the Toeplitz Algebra on the Bergman Space of the Unit Ball",
  "authors": [
    "Trieu Le"
  ],
  "comment": "8 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\mathfrak{T}$ denote the full Toeplitz algebra on the Bergman space of the unit ball $\\mathbb{B}_n.$ For each subset $G$ of $L^{\\infty},$ let $\\mathfrak{CI}(G)$ denote the closed two-sided ideal of $\\mathfrak{T}$ generated by all $T_fT_g-T_gT_f$ with $f,g\\in G.$ It is known that $\\mathfrak{CI}(C(\\bar{\\mathbb{B}}_n))=\\mathcal{K}$ - the ideal of compact operators and $\\mathfrak{CI}(C(\\mathbb{B}_n))=\\mathfrak{T}.$ Despite these ``extremal cases'', $\\mathfrak{T}$ does contain other non-trivial ideals. This paper gives a construction of a class of subsets $G$ of $L^{\\infty}$ so that $\\mathcal{K}\\subsetneq\\mathfrak{CI}(G)\\subsetneq\\mathfrak{T}.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-07T19:38:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B35"
    ],
    "keywords": [
      "unit ball",
      "bergman space",
      "full toeplitz algebra",
      "non-trivial ideals",
      "compact operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.0970L"
    }
  }
}