{
  "id": "2203.04170",
  "version": "v1",
  "published": "2022-03-08T15:58:07.000Z",
  "updated": "2022-03-08T15:58:07.000Z",
  "title": "Commutative algebras of Toeplitz operators on the Bergman space revisited: Spectral theorem approach",
  "authors": [
    "Grigori Rozenblum",
    "Nikolai Vasilevski"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "For three standard models of commutative algebras generated by Toeplitz operators in the weighted analytic Bergman space on the unit disk, we find their representations as the algebras of bounded functions of certain unbounded self-adjoint operators. We discuss main properties of these representation and, especially, describe relations between properties of the spectral function of Toeplitz operators in the spectral representation and properties of the symbols.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-08T15:58:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47L80",
      "47B35"
    ],
    "keywords": [
      "toeplitz operators",
      "spectral theorem approach",
      "commutative algebras",
      "weighted analytic bergman space",
      "representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}