{
  "id": "math/9807147",
  "version": "v1",
  "published": "1998-07-27T04:29:56.000Z",
  "updated": "1998-07-27T04:29:56.000Z",
  "title": "Compact Operators via the Berezin Transform",
  "authors": [
    "Sheldon Axler",
    "Dechao Zheng"
  ],
  "comment": "15 pages. To appear in Indiana University Mathematics Journal. For more information, see http://math.sfsu.edu/axler/CompactBerezin.html",
  "journal": "Indiana Univ. Math. J. 47 (1998), 387-400",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we prove that if S equals a finite sum of finite products of Toeplitz operators on the Bergman space of the unit disk, then S is compact if and only if the Berezin transform of S equals 0 on the boundary of the disk. This result is new even when S equals a single Toeplitz operator. Our main result can be used to prove, via a unified approach, several previously known results about compact Toeplitz operators, compact Hankel operators, and appropriate products of these operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-07-27T04:29:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B35",
      "46E20"
    ],
    "keywords": [
      "berezin transform",
      "compact operators",
      "compact hankel operators",
      "compact toeplitz operators",
      "single toeplitz operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......7147A"
    }
  }
}