{
  "id": "2312.04537",
  "version": "v1",
  "published": "2023-12-07T18:55:30.000Z",
  "updated": "2023-12-07T18:55:30.000Z",
  "title": "Crouzeix's conjecture, compressions of shifts, and classes of nilpotent matrices",
  "authors": [
    "Kelly Bickel",
    "Georgia Corbett",
    "Annie Glenning",
    "Changkun Guan",
    "Martin Vollmayr-Lee"
  ],
  "comment": "28 pages",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "This paper studies the level set Crouzeix conjecture, which is a weak version of Crouzeix's conjecture that applies to finite compressions of the shift. Amongst other results, this paper establishes the level set Crouzeix conjecture for several classes of $3\\times3$, $4\\times4$, and $5\\times5$ matrices associated to compressions of the shift via a geometric analysis of their numerical ranges. This paper also establishes Crouzeix's conjecture for several classes of nilpotent matrices whose studies are motivated by related compressions of shifts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-07T18:55:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A12",
      "47A25",
      "30J10",
      "15A60"
    ],
    "keywords": [
      "nilpotent matrices",
      "level set crouzeix conjecture",
      "establishes crouzeixs conjecture",
      "paper studies",
      "weak version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}