G-invariant norms and G(c)-radii

DOI10.1016/0024-3795(91)90168-VzbMath0722.15027OpenAlexW2079664268MaRDI QIDQ755848

Chi-Kwong Li, Nam-Kiu Tsing

Publication date: 1991

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

Full work available at URL: https://doi.org/10.1016/0024-3795(91)90168-v

zbMATH Keywords

inner product spaceunitary operatorsG-invariant normG(c)-radii

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Linear transformations, semilinear transformations (15A04)

Related Items (24)

Some aspects of the theory of norms ⋮ Permutation invariant norms ⋮ Isometries of symmetric gauge functions ⋮ Linear maps relating different unitary similarity orbits or different generalized numerical ranges ⋮ Norm hull of vectors and matrices ⋮ Norms induced by symmetric guage functions ⋮ Isometries for the induced \(c\)-norm on square matrices and some related results ⋮ Complexifications of real Banach spaces and their isometries ⋮ Chapter 7: linear preservers of relations on Matrix Spaces ⋮ A generalized numerical range: the range of a constrained sesquilinear form ⋮ C-numerical ranges andC-numerical radii ⋮ The isometries and the \(G\)-invariance of certain seminorms. ⋮ Simple Lie groups stabilizing \(G\)-invariant norms ⋮ Certain isometries on \(\mathbb{R}{}^ n\) ⋮ Lieb functions and \(m\)-positivity of norms ⋮ Congruence numerical ranges and their radii ⋮ The isometries of certain maximum norms ⋮ On \(G\)-invariant norms ⋮ On the norm property of \(G(c)\)-radii and Eaton triples ⋮ Linear operators preserving unitaryt-congruence (orthogonal similarity) on complex (real) matrices ⋮ Translation-invariant maps and applications ⋮ Coherence measures induced by norm functions ⋮ \({\mathcal S}\)-subinvariant norms ⋮ Linear operators preserving unitaryt-congruence (orthogonal similarity) on complex (real) matrices

Cites Work

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• Duality between some linear preserver problems. II: Isometries with respect to c-spectral norms and matrices with fixed singular values
• Bounded groups and norm-Hermitian matrices
• Elementary inclusion relations for generalized numerical ranges
• Norm properties of C-numerical radii
• Linear operators preserving unitarily invariant norms of matrices
• Linear operators preserving unitary similarity invariant norms
• Norms that are invariant under unitary similarities and theC-numerical radii
• Matrix Analysis
• A Simple proof of the Goldberg–Straus theorem on numerical radii
• Duality between some linear preservers problems: the invariance of thec-numerical range, thec-numerical radius and certain matrix sets
• Three elementary proofs of the goldberg-straus theorem on numerical radii
• G-Invariant Hermitian Forms and G-Invariant Elliptical Norms

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