{
  "abstract": "We use the results of Lorist and Schwenninger, {\\em A solution to Crouzeix's conjecture}, arXiv:2608.03841v2, https://arxiv.org/abs/2608.03841, to update the 2019 paper of Crouzeix and Greenbaum, {\\em Spectral sets: Numerical range and beyond}, SIAM J.~Matrix Anal.~Appl., 40(3):1087-1101. For all regions considered in the 2019 paper, we are able to show that the region is a $K$-spectral set with a bound on $K$ that is smaller than that established in the 2019 paper. In particular, we show that various annular regions are $2$-spectral sets and that a more general convex region with a circular hole or cutout is a $4$-spectral set.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22460",
  "author_total": 2,
  "authors": [
    {
      "name": "Michel Crouzeix"
    },
    {
      "name": "Anne Greenbaum"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1mp1zxdp0b4aw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22460",
  "fulltext_url": null,
  "id": "1mp1zxdp0b4aw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22460",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7214031153",
  "pdf_url": "https://arxiv.org/pdf/2609.22460",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1mp1zxdp0b4aw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.22460",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22460"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Update to: Spectral sets: Numerical range and beyond",
  "title_text": "Update to: Spectral sets: Numerical range and beyond",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/1mp1zxdp0b4aw",
  "venue": "arXiv",
  "versions": []
}