{
  "id": "1304.7936",
  "version": "v1",
  "published": "2013-04-30T09:51:25.000Z",
  "updated": "2013-04-30T09:51:25.000Z",
  "title": "Integral Representations and Decompositions of Operator Monotone Functions on the Nonnegative Reals",
  "authors": [
    "Pattrawut Chansangiam"
  ],
  "comment": "9 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we show that there is a one-to-one correspondence between operator monotone functions on the nonnegative reals and finite Borel measures on the unit interval. This correspondence appears as an integral representation of special operator monotone functions $x \\mapsto 1\\,!_t\\,x$ for $t \\in [0,1]$ with respect to a finite Borel measure on $[0,1]$, here $!_t$ denotes the $t$-weighted harmonic mean. Hence such functions form building blocks for arbitrary operator monotone functions on the nonnegative reals. Moreover, we use this integral representation to decompose operator monotone functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-30T09:51:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A63",
      "28A25"
    ],
    "keywords": [
      "integral representation",
      "nonnegative reals",
      "finite borel measure",
      "decompose operator monotone functions",
      "special operator monotone functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.7936C"
    }
  }
}