{
  "id": "2310.12857",
  "version": "v1",
  "published": "2023-10-19T16:08:26.000Z",
  "updated": "2023-10-19T16:08:26.000Z",
  "title": "Lie-Trotter means in JB-algebras",
  "authors": [
    "Zhenhua Wang"
  ],
  "comment": "17 pages, first draft",
  "categories": [
    "math.FA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We initiate the study of Lie-Trotter means in JB-algebras, which is an extension of Lie-Trotter formulas in JB-algebras. We show that the two-variable Lie-Trotter mean includes the weighted arithmetic mean, weighted harmonic mean, weighted geometric mean, and weighted spectral geometric mean. Consequently, several generalized Lie-Trotter formulas in JB-algebras are derived. Additionally, we demonstrate that the Sagae-Tanabe mean and Hansen's induction mean in JB-algebras are the multivariable Lie-Trotter mean. In the end, using arithmetic-geometric-harmonic mean inequalities we provide a characterization of the multivariate Lie-Trotter mean.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-19T16:08:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46H70",
      "47A64",
      "17C90",
      "15A16",
      "17C65",
      "81R15",
      "81P45",
      "94C99"
    ],
    "keywords": [
      "jb-algebras",
      "lie-trotter formulas",
      "arithmetic-geometric-harmonic mean inequalities",
      "hansens induction mean",
      "multivariate lie-trotter mean"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}