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

Autor:	Bickel, Kelly, Corbett, Georgia, Glenning, Annie, Guan, Changkun, Vollmayr-Lee, Martin
Rok vydání:	2023
Předmět:	Mathematics - Functional Analysis Mathematics - Complex Variables Primary 47A12 47A25 Secondary 30J10 15A60
Druh dokumentu:	Working Paper
Popis:	This paper studies the level set Crouzeix conjecture, which is a weak version of Crouzeix's conjecture that applies to finite compressions of the shift. Amongst other results, this paper establishes the level set Crouzeix conjecture for several classes of $3\times3$, $4\times4$, and $5\times5$ matrices associated to compressions of the shift via a geometric analysis of their numerical ranges. This paper also establishes Crouzeix's conjecture for several classes of nilpotent matrices whose studies are motivated by related compressions of shifts. Comment: 28 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.04537 Zobrazit plný text záznamu View this record from Arxiv