{
  "id": "2103.01866",
  "version": "v1",
  "published": "2021-03-02T17:02:02.000Z",
  "updated": "2021-03-02T17:02:02.000Z",
  "title": "The numerical range of some periodic tridiagonal operators is the convex hull of the numerical ranges of two finite matrices",
  "authors": [
    "Benjamín A. Itzá-Ortiz",
    "Rubén A. Martínez-Avendaño",
    "Hiroshi Nakazato"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we prove a conjecture stated by the first two authors in \\cite{IM} establishing the closure of the numerical range of a certain class of $n+1$-periodic tridiagonal operators as the convex hull of the numerical ranges of two tridiagonal $(n+1) \\times (n+1)$ matrices. Furthermore, when $n+1$ is odd, we show that the size of such matrices simplifies to $\\frac{n}{2}+1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-02T17:02:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A12"
    ],
    "keywords": [
      "numerical range",
      "periodic tridiagonal operators",
      "convex hull",
      "finite matrices",
      "matrices simplifies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}