Crouzeix's conjecture, compressions of shifts, and classes of nilpotent matrices

Publication Date

2024

Description

This article studies the level set Crouzeix (LSC) conjecture, which is a weak version of Crouzeix’s conjecture that applies to finite compressions of the shift. Among other results, this article establishes the LSC conjecture for several classes of 3×3 4×4, and 5×5 matrices associated with compressions of the shift via a geometric analysis of their numerical ranges. This study also establishes Crouzeix’s conjecture for several classes of nilpotent matrices whose studies are motivated by related compressions of shifts.

Journal

Concrete Operators

Volume

11

Issue

1

Department

Mathematics

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