{
  "id": "1901.07736",
  "version": "v1",
  "published": "2019-01-23T06:05:39.000Z",
  "updated": "2019-01-23T06:05:39.000Z",
  "title": "Numerical range of weighted composition operators which contain zero",
  "authors": [
    "Mahsa Fatehi",
    "Asma Negahdari"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we study when zero belongs to the numerical range of weighted composition operators $C_{\\psi,\\varphi}$ on the Fock space $\\mathcal{F}^{2}$, where $\\varphi(z)=az+b$, $a,b \\in \\mathbb{C}$ and $|a|\\leq 1$. In the case that $|a|<1$, we obtain a set contained in the numerical range of $C_{\\psi,\\varphi}$ and find the conditions under which the numerical range of $C_{\\psi,\\varphi}$ contain zero. Then for $|a|=1$, we precisely determine the numerical range of $C_{\\psi,\\varphi}$ and show that zero lies in its numerical range.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-23T06:05:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "numerical range",
      "weighted composition operators",
      "contain zero",
      "zero belongs",
      "fock space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}