{
  "id": "1801.02934",
  "version": "v1",
  "published": "2018-01-09T13:47:49.000Z",
  "updated": "2018-01-09T13:47:49.000Z",
  "title": "Unitarily invariant norm inequalities involving $G_1$ operators",
  "authors": [
    "Mojtaba Bakherad"
  ],
  "comment": "To appear in Commun. Korean Math. Society",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "In this paper, we present some upper bounds for unitarily invariant norms inequalities. Among other inequalities, we show some upper bounds for the Hilbert-Schmidt norm. In particular, we prove \\begin{align*} \\|f(A)Xg(B)\\pm g(B)Xf(A)\\|_2\\leq \\left\\|\\frac{(I+|A|)X(I+|B|)+(I+|B|)X(I+|A|)}{d_Ad_B}\\right\\|_2, \\end{align*} where $A, B, X\\in\\mathbb{M}_n$ such that $A$, $B$ are Hermitian with $\\sigma (A)\\cup\\sigma(B)\\subset\\mathbb{D}$ and $f, g$ are analytic on the complex unit disk $\\mathbb{{D}}$, $g(0)=f(0)=1$, $\\textrm{Re}(f)>0$ and $\\textrm{Re}(g)>0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-09T13:47:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unitarily invariant norm inequalities",
      "upper bounds",
      "unitarily invariant norms inequalities",
      "complex unit disk",
      "hilbert-schmidt norm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}