{
  "id": "2308.12353",
  "version": "v1",
  "published": "2023-08-23T18:01:22.000Z",
  "updated": "2023-08-23T18:01:22.000Z",
  "title": "The numerical range of periodic banded Toeplitz operators",
  "authors": [
    "Benjamín A. Itzá-Ortiz",
    "Rubén A. Martínez-Avendaño",
    "Hiroshi Nakazato"
  ],
  "comment": "17 pages, 1 figure",
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that the closure of the numerical range of a $(n+1)$-periodic and $(2m+1)$-banded Toeplitz operator can be expressed as the closure of the convex hull of the uncountable union of numerical ranges of certain symbol matrices. In contrast to the periodic $3$-banded (or tridiagonal) case, we show an example of a $2$-periodic and $5$-banded Toeplitz operator such that the closure of its numerical range is not equal to the numerical range of a single finite matrix.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-23T18:01:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A12",
      "15A60"
    ],
    "keywords": [
      "numerical range",
      "periodic banded toeplitz operators",
      "single finite matrix",
      "convex hull",
      "symbol matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}