{
  "id": "1708.04547",
  "version": "v1",
  "published": "2017-08-15T15:17:12.000Z",
  "updated": "2017-08-15T15:17:12.000Z",
  "title": "A Refinement of the operator Kantorovich inequality",
  "authors": [
    "H. R. Moradi"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We show the following result: Let $A$ be a positive operator satisfying $0<m{{\\mathbf{1}}_{\\mathcal{H}}}\\le A\\le M{{\\mathbf{1}}_{\\mathcal{H}}}$ for some scalars $m,M$ with $m<M$ and $\\Phi $ be a normalized positive linear map, then \\[\\Phi \\left( {{A}^{-1}} \\right)\\le \\Phi \\left( {{m}^{\\frac{A-M{{\\mathbf{1}}_{\\mathcal{H}}}}{M-m}}}{{M}^{\\frac{m{{\\mathbf{1}}_{\\mathcal{H}}}-A}{M-m}}} \\right)\\le \\frac{{{\\left( M+m \\right)}^{2}}}{4Mm}\\Phi {{\\left( A \\right)}^{-1}}.\\]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-15T15:17:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "operator kantorovich inequality",
      "refinement",
      "normalized positive linear map",
      "positive operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}