{
  "id": "1706.04497",
  "version": "v1",
  "published": "2017-06-14T13:58:07.000Z",
  "updated": "2017-06-14T13:58:07.000Z",
  "title": "Upper bounds for numerical radius inequalities involving off-diagonal operator matrices",
  "authors": [
    "Mojtaba Bakherad",
    "Khalid Shebrawi"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we establish some upper bounds for numerical radius inequalities including of $2\\times 2$ operator matrices and their off-diagonal parts. Among other inequalities, it is shown that if $T=\\left[\\begin{array}{cc} 0&X, Y&0 \\end{array}\\right]$, then \\begin{align*} \\omega^{r}(T)\\leq 2^{r-2}\\left\\|f^{2r}(|X|)+g^{2r}(|Y^*|)\\right\\|^\\frac{1}{2}\\left\\|f^{2r}(|Y|)+g^{2r}(|X^*|)\\right\\|^\\frac{1}{2} \\end{align*} and \\begin{align*} \\omega^{r}(T)\\leq 2^{r-2}\\left\\|f^{2r}(|X|)+f^{2r}(|Y^*|)\\right\\|^\\frac{1}{2}\\left\\|g^{2r}(|Y|)+g^{2r}(|X^*|)\\right\\|^\\frac{1}{2}, \\end{align*} where $X, Y$ are bounded linear operators on a Hilbert space ${\\mathscr H}$, $r\\geq 1$ and $f$, $g$ are nonnegative continuous functions on $[0, \\infty)$ satisfying the relation $f(t)g(t)=t\\,(t\\in[0, \\infty))$. Moreover, we present some inequalities involving the generalized Euclidean operator radius of operators $T_{1},\\cdots,T_{n}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-14T13:58:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "numerical radius inequalities",
      "off-diagonal operator matrices",
      "upper bounds",
      "generalized euclidean operator radius",
      "bounded linear operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}