Duality between some linear preservers problems: the invariance of thec-numerical range, thec-numerical radius and certain matrix sets

DOI10.1080/03081088808817888zbMath0668.15014OpenAlexW2028759239MaRDI QIDQ3820735

Chi-Kwong Li, Nam-Kiu Tsing

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1080/03081088808817888

zbMATH Keywords

linear transformationdualitylinear preserversC-numerical rangeunitary orbitC- numerical radius

Mathematics Subject Classification ID

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

Related Items (20)

Linear operators preserving the \((p,q)\) numerical radius ⋮ Some aspects of the theory of norms ⋮ Linear maps relating different unitary similarity orbits or different generalized numerical ranges ⋮ Multiplicative Preservers of C-Numerical Ranges and Radii ⋮ Duality between some linear preserver problems. II: Isometries with respect to c-spectral norms and matrices with fixed singular values ⋮ Complexifications of real Banach spaces and their isometries ⋮ Linear operators preserving unitary similarity invariant norms ⋮ Linear preservers of tensor product of unitary orbits, and product numerical range ⋮ Chapter 6: linear preservers on numerical ranges, numerical radii and unitary similarity invariant norms ⋮ A generalized numerical range: the range of a constrained sesquilinear form ⋮ C-numerical ranges andC-numerical radii ⋮ Duality between some linear preserver problems. III: c-spectral norms and (skew)-symmetric matrices with fixed singular values ⋮ Linear preserver problems: A brief introduction and some special techniques ⋮ Isometries of a generalized numerical radius ⋮ Invertible preservers and algebraic groups III: preservers of unitary similarity (congruence) invariants and overgroups of some unitary subgroups^∗ ⋮ Linear mappings preserving the diameter of the numerical range ⋮ The invarianee ofC-numerical rangeC-numericai radius, and their dual problems ⋮ Linear operators preserving the numerical range (radius) on triangular matrices ⋮ Linear operators preserving the numerical range (radius) on triangular matrices ⋮ G-invariant norms and G(c)-radii

Cites Work

• Unnamed Item
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• Rank \(k\)-preservers and preservers of sets of ranks
• Isometries of matrix algebras
• Elementary inclusion relations for generalized numerical ranges
• On certain finite dimensional numerical ranges and numerical radii^†
• The generalized spectral radius, numerical radius and spectral norm
• Linear maps on Hermitian matrices: the stabilizer of an inertia class, II
• The c-spectralc-radial and c-convex matrices
• Linear operators that preserve thec-numerical range or radius of matrices
• A theorem on numerical range
• Trace preserving linear transformations on matrix algebras
• Linear transformations on matrices

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