Michel Crouzeix

activity

20232026

collaborators

6 papers

math.NA2026

Update to: Spectral sets: Numerical range and beyond

Michel Crouzeix, Anne Greenbaum

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…

math.SP2025

Spectral estimates in the quantum annulus and in the numerical annulus

Michel Crouzeix

We improve previous estimates for matrices belonging to the quantum annulus or to the numerical annulus.

math.FA2025

Numerical Ranges and Spectral Sets: the unbounded case

Michel Crouzeix

It is known that, if $Ω$ $\subset$ C is a convex set containing the numerical range of an operator A, then $Ω$ is a C $Ω$ -spectral set for A with C $Ω$ $\leq$ 1+ $\sqrt$ 2. We impr…

math.FA2025

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

Michel Crouzeix, Anne Greenbaum

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 A…

math.FA2025

Matrices with invariant by rotation numerical ranges

Michel Crouzeix

We characterize the d x d matrices whose numerical ranges are invariant by rotations of angle 2 $π$ /d.

math.NA2023

Numerical bounds on the Crouzeix ratio for a class of matrices

Crouzeix Michel, Greenbaum Anne, Li Kenan

We provide numerical bounds on the Crouzeix ratiofor KLS matrices $A$ which have a line segment on the boundary of the numerical range. The Crouzeix ratio is the supremum over all…