{
  "id": "2204.11633",
  "version": "v1",
  "published": "2022-04-25T13:09:49.000Z",
  "updated": "2022-04-25T13:09:49.000Z",
  "title": "The polar decomposition for the product of three operators",
  "authors": [
    "Dingyi Du",
    "Qingxiang Xu",
    "Shuo Zhao"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "In the setting of adjointable operators on Hilbert $C^*$-modules, this paper deals with the polar decomposition of the product of three operators. The relationship between the polar decompositions associated with three operators is clarified. Based on this relationship, a formula for the polar decomposition of a multiplicative perturbation of an operator is provided. In addition, some characterizations of the polar decomposition associated with three operators are provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-25T13:09:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L08",
      "47A05"
    ],
    "keywords": [
      "polar decomposition",
      "relationship",
      "paper deals",
      "multiplicative perturbation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}