{
  "id": "1907.06228",
  "version": "v1",
  "published": "2019-07-14T14:36:26.000Z",
  "updated": "2019-07-14T14:36:26.000Z",
  "title": "Between the von Neumann inequality and the Crouzeix conjecture",
  "authors": [
    "Patryk Pagacz",
    "Paweł Pietrzycki",
    "Michał Wojtylak"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "A new concept of a deformed numerical range $W_q(T)$, where $T$ is a bounded linear operator or a matrix and $q\\in[0,2)$ is a parameter, is introduced. Each $W_q(T)$ is a closed convex set that contains the spectrum of $T$. Furthermore, $W_q(T)$ is decreasing with respect to $q$ and $W_1(T)$ is the numerical range. It is also shown that $W_q(T)$ is contained in the closed unit disc if and only if $T$ has a $2/(2-q)$ unitary dilation in the sense of N\\'agy-Foias. Spectral constants of $W_q(T)$ are investigated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-14T14:36:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "von neumann inequality",
      "crouzeix conjecture",
      "bounded linear operator",
      "spectral constants",
      "closed convex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}