Properties and preservers of the pseudospectrum

DOI10.1016/j.laa.2011.03.044zbMath1245.15028OpenAlexW2029353983MaRDI QIDQ651204

Chi-Kwong Li, Vincent Yannello, Virginia Forstall, Jian Lian Cui

Publication date: 8 December 2011

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

Full work available at URL: https://scholarworks.wm.edu/aspubs/1599

zbMATH Keywords

Hermitian matriceseigenvaluesorthogonal projectionsoperator normpositive semidefinite matricesunitary matricespseudospectrumpreservers

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) Linear preserver problems (15A86)

Related Items (22)

Preservers of unitary similarity functions on Lie products of matrices ⋮ Unitary similarity invariant function preservers of skew products of operators ⋮ On preservers of pseudo spectrum of skew Jordan matrix products ⋮ On the pseudo-spectra and the related properties of infinite-dimensional Hamiltonian operators ⋮ Preservers of pseudo spectral radius of operator products ⋮ Linear automorphisms of the pseudospectral unit ball ⋮ Preservers of condition spectra and pseudo spectra of Hermitian matrix Jordan products ⋮ Condition spectrum of rank one operators and preservers of the condition spectrum of skew product of operators ⋮ Linear maps preserving pseudospectrum and condition spectrum ⋮ Unnamed Item ⋮ Multiplicatively pseudo spectrum-preserving maps ⋮ Condition spectra of special operators and condition spectra preservers ⋮ The (\(n,\epsilon\))-pseudospectrum of an element of a Banach algebra ⋮ Pseudospectra of special operators and pseudospectrum preservers ⋮ On pseudospectral radii of operators on Hilbert spaces ⋮ Preservers of radial unitary similarity functions on products of operators ⋮ Nonlinear preservers of pseudospectral radius on Banach spaces ⋮ Unnamed Item ⋮ A note on preservers of pseudo spectrum of matrix products ⋮ Nonlinear maps preserving condition spectrum of Jordan skew triple product of operators ⋮ Maps preserving the pseudo spectrum of skew triple product of operators ⋮ Pseudo \(S\)-spectra of special operators in quaternionic Hilbert spaces

Uses Software

• Eigtool
• mftoolbox

Cites Work

• Unnamed Item
• Conditions for the generalized numerical range to be real
• Mappings on matrices: invariance of functional values of matrix products
• Linear Maps on Selfadjoint Operators Preserving Invertibility, Positive Definiteness, Numerical Range
• Functions of Matrices
• Automorphisms of the Complex Numbers
• Sur les transformations isométriques des espaces du type (F)
• A survey on linear preservers of numerical ranges and radii

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