{
  "id": "1903.05302",
  "version": "v1",
  "published": "2019-03-13T03:52:56.000Z",
  "updated": "2019-03-13T03:52:56.000Z",
  "title": "Isometries of absolute order unit spaces",
  "authors": [
    "Anil Kumar Karn",
    "Amit kumar"
  ],
  "comment": "10 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that for a bijective, unital, linear map between absolute order unit spaces is an isometry if, and only if, it is absolute value preserving. We deduce that, on (unital) $JB$-algebras, such maps are precisely Jordan isomorphisms. Next, we introduce the notions of absolutely matrix ordered spaces and absolute matrix order unit spaces and prove that for a bijective, unital, linear map between absolute matrix order unit spaces is a complete isometry if, and only if, it is completely absolute value preserving. We obtain that on (unital) C$^*$-algebras such maps are precisely C$^*$-algebra isomorphism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-13T03:52:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B40",
      "46L05",
      "46L30"
    ],
    "keywords": [
      "absolute order unit spaces",
      "absolute matrix order unit spaces",
      "absolute value preserving",
      "linear map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}