{
  "id": "1301.7349",
  "version": "v1",
  "published": "2013-01-30T20:18:47.000Z",
  "updated": "2013-01-30T20:18:47.000Z",
  "title": "Non-commutative f-divergence functional",
  "authors": [
    "Mohammad Sal Moslehian",
    "Mohsen Kian"
  ],
  "comment": "22 pages, to appear in Math. Nachr",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "We introduce the non-commutative $f$-divergence functional $\\Theta(\\widetilde{A},\\widetilde{B}):=\\int_TB_t^{\\frac{1}{2}}f\\left(B_t^{-\\frac{1}{2}} A_tB_t^{-\\frac{1}{2}}\\right)B_t^{\\frac{1}{2}}d\\mu(t)$ for an operator convex function $f$, where $\\widetilde{A}=(A_t)_{t\\in T}$ and $\\widetilde{B}=(B_t)_{t\\in T}$ are continuous fields of Hilbert space operators and study its properties. We establish some relations between the perspective of an operator convex function $f$ and the non-commutative $f$-divergence functional. In particular, an operator extension of Csisz\\'{a}r's result regarding $f$-divergence functional is presented. As some applications, we establish a refinement of the Choi--Davis--Jensen operator inequality, obtain some unitarily invariant norm inequalities and give some results related to the Kullback--Leibler distance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-30T20:18:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A63",
      "46L05",
      "26D15",
      "15A60",
      "60E15"
    ],
    "keywords": [
      "non-commutative f-divergence functional",
      "operator convex function",
      "hilbert space operators",
      "unitarily invariant norm inequalities",
      "choi-davis-jensen operator inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.7349S"
    }
  }
}