Similarity-preserving linear maps on \({\mathcal B}({\mathcal H})\)

DOI10.1016/S0024-3795(02)00449-4zbMath1046.47029MaRDI QIDQ1863536

Guo Xing Ji

Publication date: 11 March 2003

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

zbMATH Keywords

linear operatorelementary operatorsimilarity-preserving map

Mathematics Subject Classification ID

Commutators, derivations, elementary operators, etc. (47B47) Transformers, preservers (linear operators on spaces of linear operators) (47B49)

Related Items (19)

Similarity preserving linear maps on upper triangular matrix algebras ⋮ Certain structure of Similarity-preserving linear maps ⋮ Linear maps preserving products of positive or Hermitian matrices ⋮ Nonlinear maps preserving similarity on \(\mathcal B(H)\) ⋮ Asymptotic similarity-preserving linear maps on \(\mathcal B\)(\(\mathcal H\)) ⋮ Nonlinear maps preserving similarity on B(X) ⋮ Additive maps preserving similarity of operators on Banach spaces ⋮ Similarity invariant real linear subspaces and similarity preserving additive maps. ⋮ Asymptotic similarity preserving additive maps on \(\mathcal B(X)\) ⋮ A note on equivalence preserving maps ⋮ Linear preservers of equivalence relations on infinite-dimensional spaces ⋮ A note on unitary similarity preserving linear mappings on \(B(H)\) ⋮ Maps preserving square-zero matrices on the algebra consisting of all upper triangular matrices ⋮ Maps preserving equivalence by products of involutions ⋮ Involution similarity preserving linear maps ⋮ Similarity preserving linear maps on \(\mathscr{J}\)-subspace lattice algebras ⋮ Similarity Jordan multiplicative maps ⋮ Additive maps preserving similarity or asymptotic similarity on ⋮ Unitary similarity preserving linear maps on \(B(H)\)

Cites Work

• On operators preserving commutativity
• Spectrum-preserving linear maps
• Similarity preserving linear maps on matrices
• Linear preserver problems: A brief introduction and some special techniques
• Spectrum-preserving elementary operators on \(B(X)\)
• Linear maps preserving commutativity
• Similarity-invariant subspaces and similarity-preserving linear maps.
• Point-spectrum-preserving elementary operators on 𝐵(𝐻)
• Rank-preserving linear maps on B(X)
• Unnamed Item

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