{
  "id": "2008.10840",
  "version": "v1",
  "published": "2020-08-25T06:27:38.000Z",
  "updated": "2020-08-25T06:27:38.000Z",
  "title": "On $\\mathbb{A}$-numerical radius inequalities of operators and operator matrices",
  "authors": [
    "Raj Kumar Nayak",
    "Pintu Bhunia",
    "Kallol Paul"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\mathcal{H}$ be a complex Hilbert space and let $A$ be a positive operator on $\\mathcal{H}$. We obtain new bounds for the $A$-numerical radius of operators in semi-Hilbertican space $\\mathcal{B}_A(\\mathcal{H})$. Further, we develop inequalities for the $\\mathbb{A}$-numerical radius of $n\\times n$ operator matrices of the form $(T_{ij})_{n\\times n}$, where $T_{ij} \\in \\mathcal{B}_A(\\mathcal{H})$ and $\\mathbb{A}=\\mbox{diag}(A,A,\\ldots,A)$ is an $n\\times n$ operator diagonal matrix. Finally, we estimate bounds for the $B$-operator seminorm and $B$-numerical radius of $2\\times 2$ operator matrices, where $B=\\mbox{diag}(A,A)$. The inequalities and bounds obtained here generalize and improve on the existing ones, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-25T06:27:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A12",
      "47A30",
      "47A63"
    ],
    "keywords": [
      "operator matrices",
      "numerical radius inequalities",
      "operator diagonal matrix",
      "complex hilbert space",
      "semi-hilbertican space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}