Non-linear maps on self-adjoint operators preserving numerical radius and numerical range of Lie product

DOI10.1080/03081087.2015.1007912zbMath1336.47042arXiv1411.5891OpenAlexW2025443016WikidataQ115299604 ScholiaQ115299604MaRDI QIDQ2789397

Kan He, Jin-Chuan Hou

Publication date: 29 February 2016

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

Full work available at URL: https://arxiv.org/abs/1411.5891

zbMATH Keywords

numerical rangenumerical radiusgeneral preserversLie product of operators

Mathematics Subject Classification ID

Numerical range, numerical radius (47A12) Transformers, preservers (linear operators on spaces of linear operators) (47B49) Nonlinear operators and their properties (47H99)

Related Items (7)

Higher dimensional numerical range of Lie products on self-adjoint operators ⋮ Lie product and local spectrum preservers ⋮ Applying the theory of numerical radius of operators to obtain multi-observable quantum uncertainty relations ⋮ Higher dimensional numerical range of \(\xi\)-Lie products on bound self-adjoint operators ⋮ Unnamed Item ⋮ Recent progress on local spectrum-preserving maps ⋮ Preservers of radial unitary similarity functions on Lie products of self-adjoint operators

Cites Work

• Maps preserving numerical radius or cross norms of products of self-adjoint operators
• Mappings that preserve pairs of operators with zero triple Jordan product
• Nonlinear maps preserving numerical radius of indefinite skew products of operators
• Numerical radius preserving operators on \(C^*\)-algebras
• Linear maps preserving the closure of numerical range on nest algebras with maximal atomic nest
• Non-linear numerical radius isometries on atomic nest algebras and diagonal algebras.
• Maps leaving functional values of operator products invariant
• Maps preserving numerical ranges of operator products
• Nonlinear commutativity preserving maps on self-adjoint operators
• Mappings on matrices: invariance of functional values of matrix products
• Chapter 6: linear preservers on numerical ranges, numerical radii and unitary similarity invariant norms
• Numerical radius distance-preserving maps on $\mathcal {B}(H)$
• Maps preserving numerical radius distance on C^*-algebras
• 𝐶*-isomorphisms, Jordan isomorphisms, and numerical range preserving maps
• Product of operators and numerical range preserving maps
• On operator inequalities and linear combinations of operators

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