{
  "id": "2002.07035",
  "version": "v1",
  "published": "2020-02-17T16:26:48.000Z",
  "updated": "2020-02-17T16:26:48.000Z",
  "title": "Unified approach to spectral properties of multipliers",
  "authors": [
    "Mikael Lindström",
    "Santeri Miihkinen",
    "David Norrbo"
  ],
  "comment": "19 pages. To appear in Taiwanese J. Math",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "Let $\\mathbb B_n$ be the open unit ball in $\\mathbb C^n$. We characterize the spectra of pointwise multipliers $M_u$ acting on Banach spaces of analytic functions on $\\mathbb B_n$ satisfying some general conditions. These spaces include Bergman-Sobolev spaces $A^p_{\\alpha,\\beta}$, Bloch-type spaces $\\mathcal B_\\alpha$, weighted Hardy spaces $H^p_w$ with Muckenhoupt weights and Hardy-Sobolev Hilbert spaces $H^2_\\beta$. Moreover, we describe the essential spectra of multipliers in most of the aforementioned spaces, in particular, in those spaces for which the set of multipliers is a subset of the ball algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-17T16:26:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B35",
      "47B38"
    ],
    "keywords": [
      "spectral properties",
      "unified approach",
      "multipliers",
      "open unit ball",
      "hardy-sobolev hilbert spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}