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

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.