The normalized numerical range and the Davis-Wielandt shell

DOI10.1016/j.laa.2018.01.027zbMath1391.15076arXiv1712.01070OpenAlexW2962696617MaRDI QIDQ1743141

Siyu Zhong, Brian Lins, Ilya M. Spitkovskij

Publication date: 12 April 2018

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.01070

zbMATH Keywords

normal matrixDavis-Wielandt shellnormalized numerical range

Mathematics Subject Classification ID

Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical range, numerical radius (47A12)

Related Items

Davis-Wielandt radius inequalities for off-diagonal operator matrices ⋮ Norm-parallelism of Hilbert space operators and the Davis-Wielandt Berezin number ⋮ On the Davis–Wielandt radius inequalities of Hilbert space operators ⋮ Further refinements of Davis-Wielandt radius inequalities ⋮ Variability of paths and differential equations with \(\mathrm{BV}\)-coefficients ⋮ Between the von Neumann inequality and the Crouzeix conjecture ⋮ On the convergence of some spectral characteristics of the converging operator sequences ⋮ Joint numerical ranges: recent advances and applications minicourse by V. Müller and Yu. Tomilov ⋮ Bounds for the Davis-Wielandt radius of bounded linear operators ⋮ New inequalities for Davis-Wielandt radius of Hilbert space operators ⋮ \(a\)-numerical range on \(C^{\ast}\)-algebras ⋮ On generalized Davis-Wielandt radius inequalities of semi-Hilbertian space operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The normalized numerical ranges of \(2 \times 2\) matrices
• A derivative-coderivative inclusion in second-order nonsmooth analysis
• Convexity of the joint numerical range: Topological and differential geometric viewpoints.
• Sectorial operators and normalized numerical range.
• On eigenvalues of sums of normal matrices
• The possible shapes of numerical ranges
• An Extension of the Hausdorff-Toeplitz Theorem on the Numerical Range
• Davis-Wielandt shells of operators
• Normalized numerical ranges of some operators
• On the normalized numerical range
• On the numerical range of a matrix
• Über den Wertevorrat einer Matrix