Maps on matrix spaces

DOI10.1016/j.laa.2005.03.011zbMath1090.15002OpenAlexW2002762743MaRDI QIDQ819139

Peter Šemrl

Publication date: 22 March 2006

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

Full work available at URL: https://doi.org/10.1016/j.laa.2005.03.011

zbMATH Keywords

orthogonality preservercommutativity preservernonlinear preserversadjacency preserving mapsAutomorphismdeterminant preserverGeneral preserverGeometry of matricesinjective preserversMaps on idempotentsMatrix algebranon-additive preserversorder preserverSemigroup homomorphism

Mathematics Subject Classification ID

Related Items (34)

Adjacency preservers on invertible Hermitian matrices. I. ⋮ On preservers of pseudo spectrum of skew Jordan matrix products ⋮ On the Sylvester-like matrix equation \(AX+f(X)B=C\) ⋮ Maps from \(M_2(\mathbb F)\) to \(M_3(\mathbb F)\) that are multiplicative with respect to the Jordan triple product ⋮ Jordan triple product homomorphisms. ⋮ Lie properties in associative algebras ⋮ A Constructive Elementary Proof of the Skolem-Noether Theorem for Matrix Algebras ⋮ Preservers of eigenvalue inclusion sets of matrix products ⋮ An accelerated technique for solving the positive definite solutions of a class of nonlinear matrix equations ⋮ Multiplicative maps of matrices over rings ⋮ Automorphisms of dense subrings of the endomorphism ring of a free module ⋮ On linear preservers of permanental rank ⋮ Linear maps preserving matrices annihilated by a fixed polynomial ⋮ Adjacency preservers, symmetric matrices, and cores ⋮ General preservers of invariant subspace lattices ⋮ SCHUR MULTIPLICATIVE MAPS ON MATRICES ⋮ Spectrum and local spectrum preservers of skew Lie products of matrices ⋮ Multiplicatively pseudo spectrum-preserving maps ⋮ Recent progress on local spectrum-preserving maps ⋮ Commutativity preserving maps ⋮ Schur-multiplicative maps preserving unitarily invariant norms ⋮ Nonstandard rank-one nonincreasing maps on symmetric matrices ⋮ Strong commutativity preserving maps on Lie ideals. ⋮ Preservers of radial unitary similarity functions on products of operators ⋮ Jordan triple product homomorphisms on Hermitian matrices to and from dimension one ⋮ Additive maps on hermitian matrices ⋮ Maps completely preserving idempotents and maps completely preserving square-zero operators ⋮ Preservers of Radial unitary similarity functions on Jordan semi-triple products of self-adjoint operators ⋮ Preservers of eigenvalue inclusion sets ⋮ Mappings that preserve pairs of operators with zero triple Jordan product ⋮ Preservers of spectral radius, numerical radius, or spectral norm of the sum on nonnegative matrices ⋮ Strong commutativity preserving maps in prime rings with involution. ⋮ Preservers of radial unitary similarity functions on Lie products of self-adjoint operators ⋮ Families of Homomorphisms in Non-commutative Gelfand Theory: Comparisons and Examples

Cites Work

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• Matrix semigroup homomorphisms from dimension two to three
• Linear maps that preserve commuting pairs of matrices
• Propriétés spectrales des algèbres de Banach
• Mappings preserving spectrum and commutativity on Hermitian matrices
• Multiplicative semigroup automorphisms of upper triangular matrices over rings
• Characterization of Jordan homomorphism on \(M_ n\) using preserving properties
• Jordan triple maps.
• Generalized symmetry transformations on quaternionic indefinite inner product spaces: An extension of quaternionic version of Wigner's theorem
• Hua's fundamental theorem of the geometry of matrices.
• Wigner-type theorem on symmetry transformations in type II factors.
• An elementary proof of the fundamental theorem of projective geometry
• More on matrix semigroup homomorphisms
• Coherence invariant mappings on block triangular matrix spaces
• On Hua's fundamental theorem of the geometry of rectangular matrices
• Multiplicative mappings of operator algebras
• Nonlinear maps preserving solvability
• Commutativity preserving linear maps on central simple algebras.
• Orthogonality preserving transformations on the set of \(n\)-dimensional subspaces of a Hilbert space
• A short proof of Hua's fundamental theorem of the geometry of Hermitian matrices.
• Spectrum and commutativity preserving mappings on triangular matrices
• Additivity of Jordan maps on standard operator algebras
• Hua's fundamental theorems of the geometry of matrices and related results
• Orthogonality preserving transformations on indefinite inner product spaces: Generalization of Uhlhorn's version of Wigner's theorem
• Adjacency preserving maps on upper triangular matrix algebras
• Applying projective geometry to transformations on rank one idempotents
• Adjacency preserving mappings of rectangular matrices
• Automorphisms of \(M_{n}\), partially ordered by rank subtractivity ordering
• Adjacency preserving mappings of symmetric and Hermitian matrices
• Automorphisms of the poset of skew projections
• Maps on idempotent matrices over division rings
• Multiplicative maps of matrix semi-groups
• Representations, automorphisms, and derivations of some operator algebras
• Multiplicative maps of matrix semigroups over Dedekind rings
• On bijections that preserve complementarity of subspaces
• Automorphisms of certain groups and semigroups of matrices
• Geometry of symmetric matrices over any field with characteristic other than two
• On the geometry of algebraic homogeneous spaces
• On isomorphisms of standard operator algebras
• Additivity of *-Semigroup Isomorphisms among *-Algebras
• Jordan Homomorphisms
• Linear Transformations on Algebras of Matrices
• Jordan Homomorphisms Onto Prime Rings
• Commuting Traces of Biadditive Mappings, Commutativity-Preserving Mappings and Lie Mappings
• Multiplicative maps on invertible matrices that preserve matricial properties
• Non-Linear Spectrum-Preserving Maps
• Adjacency preserving maps on matrices and operators
• Automorphisms of the poset of upper triangular idempotent matrices
• Maps on idempotents
• Jordan Maps on Associative Algebras
• Isomorphisms of Standard Operator Algebras
• Continuous Adjacency Preserving Maps on Real Matrices
• When are Multiplicative Mappings Additive?
• Interpolation zwischen den Klassen 𝔖_p von Operatoren in Hilberträumen
• Geometries of Matrices. II. Study of Involutions in the Geometry of Symmetric Matrices
• Geometries of Matrices. III. Fundamental Theorems in the Geometries of Symmetric Matrices
• Automorphisms of the Field of Complex Numbers
• Algebraic Homogeneous Spaces over Fields of Characteristic Two
• Geometries of Matrices. I 1 Arithmetical Construction
• Preserving commutativity
• Transformations on the set of all \(n\)-dimensional subspaces of a Hilbert space preserving principal angles

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