{
  "id": "1306.0724",
  "version": "v1",
  "published": "2013-06-04T10:27:24.000Z",
  "updated": "2013-06-04T10:27:24.000Z",
  "title": "Wandering subspaces of the Bergman space and the Dirichlet space over polydisc",
  "authors": [
    "A. Chattopadhyay",
    "B. Krishna Das",
    "Jaydeb Sarkar",
    "S. Sarkar"
  ],
  "comment": "10 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Doubly commutativity of invariant subspaces of the Bergman space and the Dirichlet space over the unit polydisc $\\mathbb{D}^n$ (with $ n \\geq 2$) is investigated. We show that for any non-empty subset $\\alpha=\\{\\alpha_1,\\dots,\\alpha_k\\}$ of $\\{1,\\dots,n\\}$ and doubly commuting invariant subspace $\\s$ of the Bergman space or the Dirichlet space over $\\D^n$, the tuple consists of restrictions of co-ordinate multiplication operators $M_{\\alpha}|_\\s:=(M_{z_{\\alpha_1}}|_\\s,\\dots, M_{z_{\\alpha_k}}|_\\s)$ always possesses wandering subspace of the form \\[\\bigcap_{i=1}^k(\\s\\ominus z_{\\alpha_i}\\s). \\]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-04T10:27:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirichlet space",
      "bergman space",
      "co-ordinate multiplication operators",
      "non-empty subset",
      "tuple consists"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.0724C"
    }
  }
}