{
  "id": "1410.4905",
  "version": "v1",
  "published": "2014-10-18T03:42:49.000Z",
  "updated": "2014-10-18T03:42:49.000Z",
  "title": "Operator inequalities among arithmetic mean, geometric mean and harmonic mean",
  "authors": [
    "Shigeru Furuichi"
  ],
  "comment": "4 pages",
  "journal": "Journal of Mathematical Inequalities, Vol.8, No.3 (2014), pp.669-672",
  "doi": "10.7153/jmi-08-49",
  "categories": [
    "math.FA"
  ],
  "abstract": "We give an upper bound for the weighted geometric mean using the weighted arithmetic mean and the weighted harmonic mean. We also give a lower bound for the weighted geometric mean. These inequalities are proven for two invertible positive operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-18T03:42:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A39",
      "15A45"
    ],
    "keywords": [
      "operator inequalities",
      "weighted geometric mean",
      "lower bound",
      "upper bound",
      "weighted harmonic mean"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.4905F"
    }
  }
}