A New Proof that the Numerical Range is a Complete 2-Spectral Set for Weighted Shift Matrices
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915449198870528 |
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| author | Crouzeix, Michel Greenbaum, Anne |
| author_facet | Crouzeix, Michel Greenbaum, Anne |
| contents | In this paper we give an alternative proof that the family of matrices studied by Daeshik Choi in A proof of Crouzeix's conjecture for a class of matrices, Linear Algebra and its Applications, 438, no. 8 (2013), pp. 3247-3257, satisfy Crouzeix's conjecture. We also show that they satisfy the completely bounded version of the conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12768 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A New Proof that the Numerical Range is a Complete 2-Spectral Set for Weighted Shift Matrices Crouzeix, Michel Greenbaum, Anne Functional Analysis Numerical Analysis In this paper we give an alternative proof that the family of matrices studied by Daeshik Choi in A proof of Crouzeix's conjecture for a class of matrices, Linear Algebra and its Applications, 438, no. 8 (2013), pp. 3247-3257, satisfy Crouzeix's conjecture. We also show that they satisfy the completely bounded version of the conjecture. |
| title | A New Proof that the Numerical Range is a Complete 2-Spectral Set for Weighted Shift Matrices |
| topic | Functional Analysis Numerical Analysis |
| url | https://arxiv.org/abs/2508.12768 |