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PreprintCC BY 4.0arXiv

Update to: Spectral sets: Numerical range and beyond

  • Michel Crouzeix
  • Anne Greenbaum
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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.

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Cite

BibTeXRIS
BibTeX
@misc{crouzeix2026update,
  title = {{Update to: Spectral sets: Numerical range and beyond}},
  author = {Michel Crouzeix and Anne Greenbaum},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22460},
  eprint = {2609.22460},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22460},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Update to: Spectral sets: Numerical range and beyond
AU  - Michel Crouzeix
AU  - Anne Greenbaum
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.22460
UR  - https://arxiv.org/abs/2609.22460
AB  - 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.
ER  -