{
  "id": "2010.05826",
  "version": "v1",
  "published": "2020-10-12T16:19:47.000Z",
  "updated": "2020-10-12T16:19:47.000Z",
  "title": "Some refinements of numerical radius inequalities",
  "authors": [
    "Zahra Heydarbeygi",
    "Maryam Amyari",
    "Mahnaz Khanehgir"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we give some refinements for the second inequality in $\\frac{1}{2}\\|A\\| \\leq w(A) \\leq \\|A\\|$, where $A\\in B(H)$. In particular, if $A$ is hyponormal by refining the Young inequality with the Kantorovich constant $K(\\cdot, \\cdot)$, we show that $w(A)\\leq \\dfrac{1}{\\displaystyle {2\\inf_{\\| x \\|=1}}\\zeta(x)}\\| |A|+|A^{*}|\\|\\leq \\dfrac{1}{2}\\| |A|+|A^*|\\|$, where $\\zeta(x)=K(\\frac{\\langle |A|x,x \\rangle}{\\langle |A^{*}|x,x \\rangle},2)^{r},~~~r=\\min\\{\\lambda,1-\\lambda\\}$ and $0\\leq \\lambda \\leq 1$ . We also give a reverse for the classical numerical radius power inequality $w(A^{n})\\leq w^{n}(A)$ for any operator $A \\in B(H)$ in the case when $n=2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-12T16:19:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A12",
      "47A30",
      "47A63"
    ],
    "keywords": [
      "numerical radius inequalities",
      "refinements",
      "classical numerical radius power inequality",
      "kantorovich constant",
      "second inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}