{
  "id": "2106.11205",
  "version": "v1",
  "published": "2021-06-21T15:45:05.000Z",
  "updated": "2021-06-21T15:45:05.000Z",
  "title": "Closedness of the orbit-closed $C$-numerical range and submajorization",
  "authors": [
    "Jireh Loreaux",
    "Sasmita Patnaik"
  ],
  "comment": "19 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "For a positive trace-class operator $C$ and a bounded operator $A$, we provide an explicit description of the closure of the orbit-closed $C$-numerical range of $A$ in terms of those operators submajorized by $C$ and the essential numerical range of $A$. This generalizes and subsumes recent work of Chan, Li and Poon for the $k$-numerical range, as well as some of our own previous work on the orbit-closed $C$-numerical range.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-21T15:45:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A12",
      "47B15",
      "52A10",
      "52A40",
      "26D15"
    ],
    "keywords": [
      "closedness",
      "submajorization",
      "positive trace-class operator",
      "essential numerical range",
      "explicit description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}