Nonlinear maps preserving Lie products on factor von Neumann algebras

DOI10.1016/j.laa.2008.01.031zbMath1178.47024OpenAlexW2075871686WikidataQ115344890 ScholiaQ115344890MaRDI QIDQ927744

Fangjuan Zhang, Jian Hua Zhang

Publication date: 9 June 2008

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

Full work available at URL: https://doi.org/10.1016/j.laa.2008.01.031

zbMATH Keywords

von Neumann algebraLie productpreserver

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) Transformers, preservers (linear operators on spaces of linear operators) (47B49)

Related Items (18)

Centralizing traces and Lie triple isomorphisms on generalized matrix algebras ⋮ Maps preserving a certain product of operators ⋮ Strong 3-commutativity preserving maps on standard operator algebras ⋮ Nonlinear maps preserving Lie products on triangular algebras ⋮ A note on strong skew Jordan product preserving maps on von Neumann algebras ⋮ Maps preserving strong 2-Jordan product on some algebras ⋮ Unnamed Item ⋮ Maps preserving the square zero of η-Lie product of operators ⋮ The characterization of 2-local Lie automorphisms of some operator algebras ⋮ Maps preserving triple product on rings ⋮ Strong k-commutativity preservers on complex standard operator algebras ⋮ Nonlinear maps preserving mixed product on factors ⋮ The characterization of 2-local Lie automorphisms of some operator algebras ⋮ Unnamed Item ⋮ Nonlinear maps preserving the second mixed Lie triple products on factor von Neumann algebras ⋮ Centralizing traces and Lie-type isomorphisms on generalized matrix algebras: a new perspective ⋮ Centralizing traces and Lie triple isomorphisms on triangular algebras ⋮ Nonlinear maps preserving mixed Lie triple products on factor von Neumann algebras

Cites Work

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• Jordan mappings of semiprime rings
• Commutativity preserving linear maps on central simple algebras.
• Linear maps preserving commutativity
• Lie homomorphisms of operator algebras
• Nonlinear commutativity preserving maps on self-adjoint operators
• Commutativity Preserving Maps of Factors
• Commuting Traces of Biadditive Mappings, Commutativity-Preserving Mappings and Lie Mappings
• Commutativity Preserving Mappings of Von Neumann Algebras
• Lie Isomorphisms of Simple Rings
• Lie Isomorphisms of Factors
• Preserving commutativity

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