Zero-product preserving additive maps on symmetric operator spaces and self-adjoint operator spaces

DOI10.1016/j.laa.2004.12.002zbMath1068.47040OpenAlexW2045840544MaRDI QIDQ1772733

Jin-Chuan Hou, Lian Kuo Zhao

Publication date: 21 April 2005

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

Full work available at URL: https://doi.org/10.1016/j.laa.2004.12.002

zbMATH Keywords

symmetric operatorsself-adjoint operatorszero-product preserver

Mathematics Subject Classification ID

Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Transformers, preservers (linear operators on spaces of linear operators) (47B49)

Related Items

Additive mappings on symmetric matrices, Maps preserving the dimension of fixed points of products of operators, A characterization of an isomorphism, On the fourier algebra of certain hypergroups, Maps preserving matrix pairs with zero Jordan product, On mappings preserving zero products, Adjacency preserving maps on the space of symmetric operators, Continuous surjective maps preserving projections of Jordan products on the space of self-adjoint operators, Preserving Zeros of a Polynomial, Additive maps preserving \(r\)-nilpotent perturbation of scalars on \(B(\mathcal{H})\), Linear maps preserving zero products on nest subalgebras of von Neumann algebras, Jordan zero-product preserving additive maps on operator algebras

Cites Work

• Biseparating maps between operator algebras.
• Ring isomorphisms and linear or additive maps preserving zero products on nest algebras
• Some general techniques on linear preserver problems
• Linear maps and additive maps that preserve operators annihilated by a polynomial
• Additive idempotence preservers
• Weighted composition operators of \(C_0 (X)\)'s
• Adjacency preserving maps on the space of self-adjoint operators
• Adjacency preserving maps on the space of symmetric operators
• Mappings preserving zero products