Additive rank-one preserving mappings on triangular matrix algebras
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Publication:1573657
DOI10.1016/S0024-3795(00)00024-0zbMath0962.15002MaRDI QIDQ1573657
Jeremy Bell, Ahmed Ramzi Sourour
Publication date: 7 August 2000
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Algebraic systems of matrices (15A30) Linear transformations, semilinear transformations (15A04) Vector spaces, linear dependence, rank, lineability (15A03)
Related Items (23)
A note on additive mappings decreasing rank one ⋮ Additive preservers of numerical range ⋮ Additive mappings on symmetric matrices ⋮ Additive rank-one preservers between spaces of rectangular matrices ⋮ Permanent Polya problem for additive surjective maps ⋮ Isometries of the Toeplitz matrix algebra ⋮ Some linear preserver problems on block triangular matrix algebras ⋮ Additive mappings that do not increase minimal rank of alternate matrices ⋮ Ring isomorphisms and linear or additive maps preserving zero products on nest algebras ⋮ Additive preservers of non-zero decomposable tensors ⋮ Additive maps preserving rank-one operators on nest algebras ⋮ Rank-1 preservers on Hessenberg matrices ⋮ Linear/additive preservers of rank 2 on spaces of alternate matrices over fields ⋮ Rank-one non-increasing additive maps between block triangular matrix algebras ⋮ Geometry of rectangular block triangular matrices ⋮ Additive preservers of rank-additivity on matrix spaces ⋮ Additive rank-one preservers on block triangular matrix spaces ⋮ Geometry of block triangular matrices over a division ring ⋮ Maps preserving square-zero matrices on the algebra consisting of all upper triangular matrices ⋮ Adjacency preserving bijective maps on triangular matrices over any division ring ⋮ Spectrum and commutativity preserving mappings on triangular matrices ⋮ Coherence invariant mappings on block triangular matrix spaces ⋮ Additive rank-one preserving surjections on symmetric matrix spaces
Cites Work
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- Rank \(k\)-preservers and preservers of sets of ranks
- Transformations on tensor product spaces
- Commutativity-preserving operators on symmetric matrices
- Spectrum-preserving linear maps
- Linear transformations which preserve or decrease rank
- Linear transformations on symmetric matrices that preserve commutativity
- Spectrum-preserving additive maps
- Linear maps that preserve commuting pairs of matrices
- Linear preservers on triangular matrices
- Additive mappings preserving operators of rank one
- Linear transformations
- Linear maps preserving rank less than or equal to one
- Linear transformations on matrices: rank 1 preservers and determinant preservers
- Invertibility preserving linear maps on ℒ(𝒳)
- Linear transformations on matrices
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