{
  "id": "1207.5201",
  "version": "v1",
  "published": "2012-07-22T06:32:40.000Z",
  "updated": "2012-07-22T06:32:40.000Z",
  "title": "Characterization of the monotonicity by the inequality",
  "authors": [
    "Dinh Trung Hoa",
    "Hiroyuki Osaka",
    "Jun Tomiyama"
  ],
  "comment": "10 pages",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Let $\\varphi$ be a normal state on the algebra $B(H)$ of all bounded operators on a Hilbert space $H$, $f$ a strictly positive, continuous function on $(0, \\infty)$, and let $g$ be a function on $(0, \\infty)$ defined by $g(t) = \\frac{t}{f(t)}$. We will give characterizations of matrix and operator monotonicity by the following generalized Powers-St\\ormer inequality: $$ \\varphi(A + B) - \\varphi(|A - B|) \\leq 2\\varphi(f(A)^1/2g(B)f(A)^1/2), $$ whenever $A, B$ are positive invertible operators in $B(H).$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-22T06:32:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L30",
      "15A45"
    ],
    "keywords": [
      "characterization",
      "inequality",
      "normal state",
      "hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.5201H"
    }
  }
}