Continuity properties of vectors realizing points in the classical field of values

DOI10.1080/03081087.2012.736991zbMath1290.15012arXiv1307.5033OpenAlexW2963424254MaRDI QIDQ2872502

Charles R. Johnson, Brian Lins, Ryan Kirk, Dan Corey, Ilya M. Spitkovskij

Publication date: 15 January 2014

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

Full work available at URL: https://arxiv.org/abs/1307.5033

zbMATH Keywords

numerical examplesnumerical rangemetric spacefield of valuesweak continuitymulti-valued mappinginverse continuity

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Weak and generalized continuity (54C08) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical range, numerical radius (47A12)

Related Items (6)

Pre-images of extreme points of the numerical range, and applications ⋮ Maximum-entropy inference and inverse continuity of the numerical range ⋮ Signatures of quantum phase transitions from the boundary of the numerical range ⋮ Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach ⋮ Continuous selections of the inverse numerical range map ⋮ Inverse continuity of the numerical range map for Hilbert space operators

Cites Work

• Ratio numerical ranges of operators
• The constrained bilinear form and the C-numerical range
• Equality of higher numerical ranges of matrices and a conjecture of Kippenhahn on Hermitian pencils
• A simple algorithm for the inverse field of values problem
• The Toeplitz-Hausdorff Theorem Explained

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