{
  "id": "1609.08909",
  "version": "v1",
  "published": "2016-09-28T13:49:05.000Z",
  "updated": "2016-09-28T13:49:05.000Z",
  "title": "Log-majorization and Lie-Trotter formula for the Cartan barycenter on probability measure spaces",
  "authors": [
    "Fumio Hiai",
    "Yongdo Lim"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We extend Ando-Hiai's log-majorization for the weighted geometric mean of positive definite matrices into that for the Cartan barycenter in the general setting of probability measures on the Riemannian manifold of positive definite matrices equipped with trace metric. We also derive a version of Lie-Trotter formula and related unitarily invariant norm inequalities for the Cartan barycenter as the main application of log-majorization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-28T13:49:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A42",
      "47A64",
      "47B65",
      "47L07"
    ],
    "keywords": [
      "cartan barycenter",
      "probability measure spaces",
      "lie-trotter formula",
      "positive definite matrices",
      "related unitarily invariant norm inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}