{
  "id": "1909.12883",
  "version": "v1",
  "published": "2019-09-27T19:29:01.000Z",
  "updated": "2019-09-27T19:29:01.000Z",
  "title": "Multipliers and operator space structure of weak product spaces",
  "authors": [
    "Raphaël Clouâtre",
    "Michael Hartz"
  ],
  "comment": "21 pages",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "In the theory of reproducing kernel Hilbert spaces, weak product spaces generalize the notion of the Hardy space $H^1$. For complete Nevanlinna-Pick spaces $\\mathcal H$, we characterize all multipliers of the weak product space $\\mathcal H \\odot \\mathcal H$. In particular, we show that if $\\mathcal H$ has the so-called column-row property, then the multipliers of $\\mathcal H$ and of $\\mathcal H \\odot \\mathcal H$ coincide. This result applies in particular to the classical Dirichlet space and to the Drury-Arveson space on a finite dimensional ball. As a key device, we exhibit a natural operator space structure on $\\mathcal H \\odot \\mathcal H$, which enables the use of dilations of completely bounded maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-27T19:29:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E22",
      "46L07",
      "47A20"
    ],
    "keywords": [
      "multipliers",
      "natural operator space structure",
      "complete nevanlinna-pick spaces",
      "reproducing kernel hilbert spaces",
      "finite dimensional ball"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}