{
  "id": "2105.07760",
  "version": "v3",
  "published": "2021-05-17T12:11:55.000Z",
  "updated": "2022-05-31T15:31:32.000Z",
  "title": "Multiplication by a finite Blaschke product on weighted Bergman spaces: commutant and reducing subspaces",
  "authors": [
    "Eva A. Gallardo-Gutiérrez",
    "Jonathan R. Partington"
  ],
  "comment": "13 pages; some typos fixed and reference updated",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "We provide a characterization of the commutant of analytic Toeplitz operators $T_B$ induced by finite Blachke products $B$ acting on weighted Bergman spaces which, as a particular instance, yields the case $B(z)=z^n$ on the Bergman space solved recently by by Abkar, Cao and Zhu. Moreover, it extends previous results by Cowen and Wahl in this context and applies to other Banach spaces of analytic functions such as Hardy spaces $H^p$ for $1<p<\\infty$. Finally, we apply this approach to study the reducing subspaces of $T_{B}$ in weighted Bergman spaces.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-05-31T15:31:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A15",
      "47A55",
      "47B15"
    ],
    "keywords": [
      "weighted bergman spaces",
      "finite blaschke product",
      "reducing subspaces",
      "multiplication",
      "finite blachke products"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}