{
  "id": "1212.5690",
  "version": "v1",
  "published": "2012-12-22T13:40:21.000Z",
  "updated": "2012-12-22T13:40:21.000Z",
  "title": "On an operator Kantorovich inequality for positive linear maps",
  "authors": [
    "Minghua Lin"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We improve the operator Kantorovich inequality as follows: Let $A$ be a positive operator on a Hilbert space with $0<m\\le A \\le M$. Then for every unital positive linear map $\\Phi$, \\[\\Phi(A^{-1})^2\\le (\\frac{(M+m)^2}{4Mm})^2\\Phi(A)^{-2}.\\] As a consequence, \\[\\Phi(A^{-1})\\Phi(A)+\\Phi(A)\\Phi(A^{-1}) \\le \\frac{(M+m)^2}{2Mm}.\\]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-22T13:40:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "operator kantorovich inequality",
      "unital positive linear map",
      "hilbert space",
      "positive operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.5690L"
    }
  }
}