{
  "id": "math/0702475",
  "version": "v1",
  "published": "2007-02-16T08:32:42.000Z",
  "updated": "2007-02-16T08:32:42.000Z",
  "title": "A matrix subadditivity inequality for f(A+B) and f(A)+f(B)",
  "authors": [
    "Jean-Christophe Bourin",
    "Mitsuru Uchiyama"
  ],
  "comment": "accepted in LAA",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Let f be a non-negative concave function on the positive half-line. Let A and B be two positive matrices. Then, for all symmetric norms, || f(A+B) || is less than || f(A)+f(B) ||. When f is operator concave, this was proved by Ando and Zhan. Our method is simpler. Several related results are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-16T08:32:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A30",
      "47A63"
    ],
    "keywords": [
      "matrix subadditivity inequality",
      "operator concave",
      "symmetric norms",
      "non-negative concave function",
      "positive half-line"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2475B"
    }
  }
}