{
  "id": "2102.01953",
  "version": "v1",
  "published": "2021-02-03T09:04:42.000Z",
  "updated": "2021-02-03T09:04:42.000Z",
  "title": "Furtherance of Numerical radius inequalities of Hilbert space operators",
  "authors": [
    "Pintu Bhunia",
    "Kallol Paul"
  ],
  "comment": "9 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "If $A,B$ are bounded linear operators on a complex Hilbert space, then % $w(A) \\leq \\frac{1}{2}\\left( \\|A\\|+\\sqrt{r\\left(|A||A^*|\\right)}\\right)$ and $w(AB \\pm BA)\\leq 2\\sqrt{2}\\|B\\|\\sqrt{ w^2(A)-\\frac{c^2(\\Re (A))+c^2(\\Im (A))}{2} },$ \\begin{eqnarray*} w(A) &\\leq& \\frac{1}{2}\\left( \\|A\\|+\\sqrt{r\\left(|A||A^*|\\right)}\\right),\\\\ w(AB \\pm BA)&\\leq& 2\\sqrt{2}\\|B\\|\\sqrt{ w^2(A)-\\frac{c^2(\\Re (A))+c^2(\\Im (A))}{2} }, \\end{eqnarray*} where $w(.),\\|.\\|,c(.)$ and $r(.)$ are the numerical radius, the operator norm, the Crawford number and the spectral radius respectively, and $\\Re (A)$, $\\Im (A)$ are the real part, the imaginary part of $A$ respectively. The inequalities obtained here generalize and improve on the existing well known inequalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-03T09:04:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A12",
      "47A30"
    ],
    "keywords": [
      "hilbert space operators",
      "numerical radius inequalities",
      "furtherance",
      "complex hilbert space",
      "real part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}