{
  "id": "2207.01007",
  "version": "v1",
  "published": "2022-07-03T10:52:31.000Z",
  "updated": "2022-07-03T10:52:31.000Z",
  "title": "Numerical radius and Berezin number inequality",
  "authors": [
    "Satyabrata Majee",
    "Amit Maji",
    "Atanu Manna"
  ],
  "comment": "Preliminary version, 22 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study various inequalities for numerical radius and Berezin number of a bounded linear operator on a Hilbert space. It is proved that the numerical radius of a pure two-isometry is 1 and the Crawford number of a pure two-isometry is 0. In particular, we show that for any scalar-valuednon-constant inner function $\\theta$, the numerical radius and the Crawford number of a Toeplitz operator $T_{\\theta}$ on a Hardy space is 1 and 0, respectively. It is also shown that numerical radius is multiplicative for a class of isometries and sub-multiplicative for a class of commutants of a shift. We have illustrated these results with some concrete examples. Finally, some Hardy-type inequalities for Berezin number of certain class of operators are established with the help of the classical Hardy's inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-03T10:52:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A12",
      "47A63"
    ],
    "keywords": [
      "numerical radius",
      "berezin number inequality",
      "pure two-isometry",
      "crawford number",
      "scalar-valuednon-constant inner function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}