{
  "id": "1610.03869",
  "version": "v1",
  "published": "2016-10-12T20:37:27.000Z",
  "updated": "2016-10-12T20:37:27.000Z",
  "title": "Unitarily invariant norm inequalities for elementary operators involving $G_{1}$ operators",
  "authors": [
    "Fuad Kittaneh",
    "Mohammad Sal Moslehian",
    "Mohammad Sababheh"
  ],
  "comment": "11 pages; to appear in Linear Algebra Appl. (LAA)",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "In this paper, motivated by perturbation theory of operators, we present some upper bounds for $|||f(A)Xg(B)+ X|||$ in terms of $|||\\,|AXB|+|X|\\,|||$ and $|||f(A)Xg(B)- X|||$ in terms of $|||\\,|AX|+|XB|\\,|||$, where $A, B$ are $G_{1}$ operators, $|||\\cdot|||$ is a unitarily invariant norm and $f, g$ are certain analytic functions. Further, we find some new upper bounds for the the Schatten $2$-norm of $f(A)X\\pm Xg(B)$. Several special cases are discussed as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-12T20:37:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A60",
      "30E20",
      "47A30",
      "47B10",
      "47B15",
      "47B20"
    ],
    "keywords": [
      "unitarily invariant norm inequalities",
      "elementary operators",
      "upper bounds",
      "perturbation theory",
      "analytic functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}