{
  "id": "2306.06685",
  "version": "v1",
  "published": "2023-06-11T13:59:47.000Z",
  "updated": "2023-06-11T13:59:47.000Z",
  "title": "An extension of the weighted geometric mean in unital $JB$-algebras",
  "authors": [
    "Amir Ghasem Ghazanfari",
    "Somayeh Malekinejad"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\mathcal{A}$ be a unital $JB$-algebra and $A,~B\\in\\mathcal{A}$, we extend the weighted geometric mean $A\\sharp_r B$, from $r\\in [0,1]$ to $r\\in (-1, 0)\\cup(1, 2)$. We will notice that many results will be reversed when the domain of $r$ change from $[0,1]$ to $(-1,0)$ or $(1,2)$. We investigate some property of $A\\sharp_r B$ for such quantities of $r$, such as we show that $A\\sharp_r B$ is separately operator convex with respect to $A, B$. We also introduce the Heinz and Heron means for unital $JB$-algebras and give some famous inequalities involving them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-11T13:59:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weighted geometric mean",
      "separately operator convex",
      "heron means",
      "quantities",
      "famous inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}