{
  "id": "1109.0305",
  "version": "v3",
  "published": "2011-09-01T21:03:34.000Z",
  "updated": "2012-05-17T14:57:45.000Z",
  "title": "Compactness characterization of operators in the Toeplitz algebra of the Fock space $F_α^p$",
  "authors": [
    "Wolfram Bauer",
    "Joshua Isralowitz"
  ],
  "comment": "v1: 36 pages, no figures v2: 36 pages, no figures, typos corrected, submitted v3: 41 pages, no figures, typos corrected, major revisions made (Proposition 3.6 of v2 generalised significantly and introduction/closing remarks changed significantly), to appear in the Journal of Functional Analysis",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "For $1 < p < \\infty$ let $\\mathcal{T}_p ^\\alpha$ be the norm closure of the algebra generated by Toeplitz operators with bounded symbols acting on the standard weighted Fock space $F_\\alpha ^p$. In this paper, we will show that an operator $A$ is compact on $F_\\alpha ^p$ if and only if $A \\in \\mathcal{T}_p ^\\alpha$ and the Berezin transform $B_\\alpha (A)$ of $A$ vanishes at infinity.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-05-17T14:57:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B35",
      "30H20"
    ],
    "keywords": [
      "toeplitz algebra",
      "compactness characterization",
      "standard weighted fock space",
      "toeplitz operators",
      "berezin transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.0305B"
    }
  }
}