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arXiv · 2508.12768

A New Proof that the Numerical Range is a Complete 2-Spectral Set for Weighted Shift Matrices

Michel Crouzeix·Anne Greenbaum
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Abstract

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.

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Michel Crouzeix, Anne Greenbaum. 2025-08-18. A New Proof that the Numerical Range is a Complete 2-Spectral Set for Weighted Shift Matrices. https://arxiv.org/abs/2508.12768

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