Some Extensions of the Crouzeix--Palencia Result

DOI10.1137/17M1140832zbMath1392.15029arXiv1707.08603OpenAlexW2963580980WikidataQ129850323 ScholiaQ129850323MaRDI QIDQ4643329

Trevor Caldwell, Kenan Li, Anne Greenbaum

Publication date: 24 May 2018

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.08603

zbMATH Keywords

numerical rangespectral setCrouzeix's conjecture

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical range, numerical radius (47A12) Spectral sets of linear operators (47A25)

Related Items

Spectral sets, extremal functions and exceptional matrices ⋮ On the uniqueness of functions that maximize the Crouzeix ratio ⋮ Between the von Neumann inequality and the Crouzeix conjecture ⋮ Joint numerical ranges: recent advances and applications minicourse by V. Müller and Yu. Tomilov ⋮ Remarks on the Crouzeix--Palencia Proof that the Numerical Range is a (1+\sqrt2)-Spectral Set ⋮ Crouzeix's conjecture and related problems ⋮ Dilation theory in finite dimensions and matrix convexity ⋮ Spectral Sets: Numerical Range and Beyond

Cites Work

• Unnamed Item
• Unnamed Item
• Numerical range and functional calculus in Hilbert space
• Constants related to operators of class \(C_\rho\)
• Finite Blaschke product interpolation on the closed unit disc
• Bounds for analytical functions of matrices
• A proof of Crouzeix's conjecture for a class of matrices
• The variation of the spectrum of a normal matrix
• A Note on Bounded Interpolation in the Unit Disc
• Remarks on the Crouzeix--Palencia Proof that the Numerical Range is a (1+\sqrt2)-Spectral Set
• Crouzeix's Conjecture Holds for Tridiagonal 3 x 3 Matrices with Elliptic Numerical Range Centered at an Eigenvalue
• Generalization of von Neumann's spectral sets and integral representation of operators
• The Numerical Range is a $(1+\sqrt{2})$-Spectral Set