{
  "id": "1207.2025",
  "version": "v1",
  "published": "2012-07-09T12:54:41.000Z",
  "updated": "2012-07-09T12:54:41.000Z",
  "title": "Infinitely divisible metrics and curvature inequalities for operators in the Cowen-Douglas class",
  "authors": [
    "Shibananda Biswas",
    "Dinesh Kumar Keshari",
    "Gadadhar Misra"
  ],
  "comment": "14 pages",
  "doi": "10.1112/jlms/jdt045",
  "categories": [
    "math.FA"
  ],
  "abstract": "The curvature $\\mathcal K_T(w)$ of a contraction $T$ in the Cowen-Douglas class $B_1(\\mathbb D)$ is bounded above by the curvature $\\mathcal K_{S^*}(w)$ of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this note, we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions on the metric of the holomorphic Hermitian vector bundle $E_T$ corresponding to the operator $T$ in the Cowen-Douglas class $B_1(\\mathbb D)$ which ensures negative definiteness of the curvature function. We obtain a generalization for commuting tuples of operators in the class $B_1(\\Omega)$, for a bounded domain $\\Omega$ in $\\mathbb C^m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-09T12:54:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B32",
      "47B35"
    ],
    "keywords": [
      "cowen-douglas class",
      "curvature inequality",
      "infinitely divisible metrics",
      "holomorphic hermitian vector bundle",
      "stronger form"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.2025B"
    }
  }
}