A New Proof that the Numerical Range is a Complete 2-Spectral Set for Weighted Shift Matrices
Functional Analysis
2025-08-19 v1 Numerical Analysis
Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2508.12768,
title = {A New Proof that the Numerical Range is a Complete 2-Spectral Set for Weighted Shift Matrices},
author = {Michel Crouzeix and Anne Greenbaum},
journal= {arXiv preprint arXiv:2508.12768},
year = {2025}
}