{
  "id": "2107.07935",
  "version": "v1",
  "published": "2021-07-16T14:51:03.000Z",
  "updated": "2021-07-16T14:51:03.000Z",
  "title": "A note on the parallel sum",
  "authors": [
    "Frank Hansen"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "By using a variational principle we find a necessary and sufficient condition for an operator to majorise the parallel sum of two positive definite operators. This result is then used as a vehicle to create new operator inequalities involving the parallel sum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-16T14:51:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A63"
    ],
    "keywords": [
      "parallel sum",
      "variational principle",
      "sufficient condition",
      "positive definite operators",
      "operator inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}