{
  "id": "2409.04444",
  "version": "v1",
  "published": "2024-08-19T12:42:59.000Z",
  "updated": "2024-08-19T12:42:59.000Z",
  "title": "A Note on the Carathéodory Number of the Joint Numerical Range",
  "authors": [
    "Beatrice Maier",
    "Tim Netzer"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that the Carath\\'{e}odory number of the joint numerical range of $d$ many bounded self-adjoint operators is at most $d-1$, and even at most $d-2$ if the underlying Hilbert space has dimension at least $3$. This extension of the classical convexity results for numerical ranges shows that also joint numerical ranges are significantly less non-convex than general sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-19T12:42:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "joint numerical range",
      "carathéodory number",
      "bounded self-adjoint operators",
      "hilbert space",
      "classical convexity results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}