On maps preserving products of matrices

DOI10.1016/j.laa.2018.10.029zbMath1430.15021OpenAlexW2899349492MaRDI QIDQ1713305

Regan Kapalko, Samuel Hsu, Louisa Catalano

Publication date: 24 January 2019

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

Full work available at URL: https://doi.org/10.1016/j.laa.2018.10.029

zbMATH Keywords

Jordan productmatrices over division ringsmaps preserving products

Mathematics Subject Classification ID

Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Linear transformations, semilinear transformations (15A04) Linear preserver problems (15A86) Functional identities (associative rings and algebras) (16R60)

Related Items (13)

Linear bijective maps preserving fixed values of products of matrices at fixed vectors ⋮ On maps preserving products equal to fixed elements ⋮ Fixed product preserving mappings on Banach algebras ⋮ Weighted Jordan homomorphisms ⋮ Bilinear maps on C*-algebras that have product property at a compact element ⋮ Linear bijective maps preserving fixed products of matrices ⋮ On maps preserving Lie products equal to a rank-one nilpotent ⋮ Pairs of linear maps on matrix spaces preserving products equal to fixed elements ⋮ Linear maps preserving products equal to primitive idempotents of an incidence algebra ⋮ On maps preserving products equal to a rank-one idempotent ⋮ On maps preserving rank-one nilpotents ⋮ On maps preserving products equal to a diagonalizable matrix ⋮ On maps preserving square roots of idempotent and rank-one nilpotent matrices

Cites Work

• On maps preserving zero Jordan products.
• On maps characterized by action on equal products
• Maps characterized by action on zero products.
• Hua's theorem for simple Artin algebras
• On maps preserving square-zero matrices.
• On Maps Preserving Products
• A NOTE ON 2-LOCAL MAPS
• Linear mappings preserving square-zero matrices
• Linear maps on von Neumann algebras preserving zero products on tr-rank
• Characterizations of Jordan mappings on some rings and algebras through zero products
• Square roots of complex matrices
• Characterizing homomorphisms, derivations and multipliers in rings with idempotents

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