Some linear preserver problems on upper triangular matrices

DOI10.1080/03081089808818586zbMath0974.15001OpenAlexW2062778691MaRDI QIDQ4942585

Peter Šemrl, Lajos Molnár

Publication date: 30 November 2001

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

Full work available at URL: https://doi.org/10.1080/03081089808818586

zbMATH Keywords

linear preserverrankupper triangular matricescommutativityrank-one matricesrank-one idempotents

Mathematics Subject Classification ID

Commutativity of matrices (15A27) Linear transformations, semilinear transformations (15A04) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (31)

Jordan isomorphisms on nest subalgebras ⋮ Linear maps on von Neumann algebras preserving zero products on tr-rank ⋮ Maps on infinite triangular matrices preserving idempotents ⋮ Additive mappings on von Neumann algebras preserving absolute values ⋮ Rank-1 preserving linear maps on nest algebras. ⋮ Some linear preserver problems on block triangular matrix algebras ⋮ Jordan homomorphisms of upper triangular matrix rings. ⋮ Jordan isomorphisms of generalized structural matrix rings ⋮ Additive maps preserving rank-one operators on nest algebras ⋮ Injective strong commutativity preservers on \(\mathcal{T}_{\infty}(F)\) ⋮ Jordan homomorphisms of upper triangular matrix rings over a prime ring. ⋮ Rank-one nonincreasing mappings on triangular matrices and some related preserver problems ⋮ Automorphisms of the poset of upper triangular idempotent matrices ⋮ Order preserving maps on the poset of upper triangular idempotent matrices ⋮ Rank-one non-increasing additive maps between block triangular matrix algebras ⋮ Jordan derivations and antiderivations on triangular matrices ⋮ Additive rank-one preservers on block triangular matrix spaces ⋮ Linear maps preserving idempotence on nest algebras ⋮ Jordan isomorphisms of 2-torsionfree triangular rings ⋮ Linear preservers on upper triangular operator matrix algebras ⋮ Modular automorphisms preserving idempotence and Jordan isomorphisms of triangular matrices over commutative rings ⋮ Additivity of Jordan maps on triangular algebras ⋮ Jordan isomorphisms of upper triangular matrix rings. ⋮ Jordan isomorphisms of finitary incidence algebras ⋮ Potent preservers of incidence algebras ⋮ Jordan isomorphisms of skew incidence rings ⋮ Jordan isomorphisms of triangular matrix algebras over a connected commutative ring ⋮ Linear maps preserving zero products on nest subalgebras of von Neumann algebras ⋮ Spectrum and commutativity preserving mappings on triangular matrices ⋮ Coherence invariant mappings on block triangular matrix spaces ⋮ Jordan higher derivable maps on triangular algebras by commutative zero products

Cites Work

• A note on algebra automorphisms of triangular matrices over commutative rings
• Linear preserver problems: A brief introduction and some special techniques
• Linear preservers on triangular matrices
• Linear maps preserving commutativity
• Rigid Embedding of Simple Groups in the General Linear Group
• Invariants of linear maps on matrix algebras

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