Maps on Matrix Algebras Preserving Commutativity

DOI10.1080/03081080310001609992zbMath1059.15003OpenAlexW2003607621MaRDI QIDQ4825457

Peter Šemrl, Gregor Dolinar

Publication date: 28 October 2004

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

Full work available at URL: https://doi.org/10.1080/03081080310001609992

zbMATH Keywords

matrix algebrascommutativity preserving map

Mathematics Subject Classification ID

Commutativity of matrices (15A27) Algebraic systems of matrices (15A30) Linear transformations, semilinear transformations (15A04)

Related Items (12)

Maps onB(H) Preserving Idempotents ⋮ Extremal generalized centralizers in matrix algebras ⋮ Extremal matrix centralizers ⋮ Nonlinear strong commutativity preserving maps on skew elements of prime rings with involution. ⋮ Maps preserving the local spectrum of Jordan product of matrices ⋮ Injective strong commutativity preservers on \(\mathcal{T}_{\infty}(F)\) ⋮ Continuous maps on triangular matrices that preserve commutativity ⋮ Maps preserving the local spectrum of triple product of operators ⋮ Strong commutativity preserving generalized derivations on Lie ideals ⋮ Maps on \({\mathcal B}({\mathcal H})\) preserving involution ⋮ Strong commutativity preserving derivations on Lie ideals of prime Γ-rings ⋮ Strong commutativity preserving maps in prime rings with involution.

Cites Work

• Commutativity-preserving operators on symmetric matrices
• On operators preserving commutativity
• Linear transformations on symmetric matrices that preserve commutativity
• Linear maps that preserve commuting pairs of matrices
• Lipschitz spectrum preserving mappings on algebras of matrices
• Determinant preserving maps on matrix algebras
• Linear maps preserving commutativity
• Hua's fundamental theorems of the geometry of matrices and related results
• Geometry of symmetric matrices over any field with characteristic other than two
• Commutativity Preserving Maps of Factors
• Commuting Traces of Biadditive Mappings, Commutativity-Preserving Mappings and Lie Mappings
• Linear transformations on matrices: The invariance of commuting pairs of matrices
• Invariants of linear maps on matrix algebras
• Commutativity Preserving Mappings of Von Neumann Algebras
• Additive mappings preserving commutativity
• Preserving commutativity

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