Some general techniques on linear preserver problems

DOI10.1016/S0024-3795(00)00119-1zbMath0964.15004WikidataQ127109585 ScholiaQ127109585MaRDI QIDQ1583717

Chi-Kwong Li, Peter Šemrl, Alexander E. Guterman

Publication date: 19 July 2001

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

zbMATH Keywords

matrix algebranilpotent matriceslinear preserver problemsidempotent preserverrank-preserving linear mappings

Mathematics Subject Classification ID

Algebraic systems of matrices (15A30) Linear transformations, semilinear transformations (15A04)

Related Items

Similarity preserving linear maps on upper triangular matrix algebras, Maps preserving some spectral domains of skew products of operators, Linear/additive preservers of ranks 2 and 4 on alternate matrix spaces over fields, Linear rank preservers of tensor products of rank one matrices, Linear operators preserving combinatorial matrix sets, Unnamed Item, Linear maps preserving the set of Fredholm operators, Maps onB(H) Preserving Idempotents, Additive Maps Preserving Moore–Penrose Inverses of Matrices on Symmetric Matrix Spaces, Linear preservers of quadratic operators, Certain structure of Similarity-preserving linear maps, Linear maps preserving products of positive or Hermitian matrices, Preservers of restricted unitary orbits of projections, A localization technique for linear preserver problems, Linear maps preserving regularity in \(C^*\)-algebras, Additive preservers of Drazin invertible operators with bounded index, Linear preservers on idempotents of Fourier algebras, Asymptotic similarity-preserving linear maps on \(\mathcal B\)(\(\mathcal H\)), Biseparating maps between operator algebras., Bijections preserving commutators and automorphisms of unitriangular groups, Jordan product and fixed points preservers, Linear maps preserving matrices annihilated by a fixed polynomial, Maps on matrix algebras preserving idempotents, Adjacency preservers, symmetric matrices, and cores, Linear maps preserving inclusion of fixed subsets into the spectrum, Linear maps preserving Pareto eigenvalues, Hua's fundamental theorem of the geometry of matrices., Additive maps preserving Jordan zero-products on nest algebras, \(c\)-Numerical radius isometries on matrix algebras and triangular matrix algebras, Maps preserving the diamond partial order, Linear maps on \(M_{n}(\mathbb C)\) preserving the local spectrum, Linear preservers of weak majorization on \(\ell^{1}(I)^{+}\), when \(I\) is an infinite set, Additive rank-1 preservers between spaces of Hermitian matrices, Injective strong commutativity preservers on \(\mathcal{T}_{\infty}(F)\), Automorphisms of the poset of upper triangular idempotent matrices, A note on unitary similarity preserving linear mappings on \(B(H)\), Operators preserving the strong Birkhoff-James orthogonality on \(\mathbf{B}(H)\), LINEAR PRESERVERS FOR DRAZIN STAR PARTIAL ORDER, Additive preservers of rank-additivity on matrix spaces, Linear preservers for matrix inequalities and partial orderings, Zero-product preserving additive maps on symmetric operator spaces and self-adjoint operator spaces, Additive preservers of rank on alternate matrix spaces over fields and applications, Rank one preserving \(\mathbb R\)-linear maps on spaces of self-adjoint operators on complex Hilbert spaces, Geometry of block triangular matrices over a division ring, Linear maps transforming the higher numerical ranges, Linear maps preserving semi-Fredholm operators and generalized invertibility, Maps preserving the idempotency of products of operators, Additive Drazin inverse preservers, On linear maps preserving complex symmetry, Preservers of maximally entangled states, Complex symmetric operators and additive preservers problem, Linear preservers of DSS-weak majorization on discrete Lebesgue space , when I is an infinite set, A note on linear preservers on semipositive and minimal semipositive matrices, Nonlinear preservers involving quadratic operators, Maps preserving semi-Fredholm operators on Hilbert \(C^*\)-modules, Maps preserving absolute continuity and singularity of positive operators, Additive adjoint preservers between matrix spaces, Maps on \({\mathcal B}({\mathcal H})\) preserving involution, Linear maps preserving Fredholm and Atkinson elements ofC*-algebras, Characterizing operations preserving separability measures via linear preserver problems, Additive preservers of idempotence and Jordan homorphisms between rings of square matrices, Preserving Zeros of a Polynomial, Linear mappings preserving the copositive cone, Mappings preserving spectra of products of matrices, On operators preserving James' orthogonality, Linear maps preserving the minimum and reduced minimum moduli, On the preservers of maximally entangled states, Bijective maps of infinite triangular and unitriangular matrices preserving commutators, Linear maps preserving zero products on nest subalgebras of von Neumann algebras, Nonlinear preservers problem of complex symmetric operators, Additive idempotence preservers, Linear transformations between matrix spaces that map one rank specific set into another, Additive rank-one preserving surjections on symmetric matrix spaces, Linear mappings preserving the completely positive rank

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Complete theories
• All linear operators leaving the unitary group invariant
• Transformations on tensor product spaces
• Similarity preserving linear maps on matrices
• Automorphisms of \(\det (X_{ij}):\) The group scheme approach
• Linear maps that preserve matrices annihilated by a polynomial
• A generalization of the Motzkin-Taussky theorem
• Fast projection methods for minimal design problems in linear system theory
• \(C^*\)-algebras of real rank zero
• Linear preserver problems: A brief introduction and some special techniques
• Linear maps on algebraic groups
• Model theoretic algebra. Selected topics
• Linear maps that preserve singular and nonsingular matrices
• Spectral characterization of idempotents and invertibility preserving linear maps
• Overgroups of some classical linear groups with applications to linear preserver problems
• Spaces of symmetric matrices of bounded rank
• Invertibility preserving maps preserve idempotents
• Linear preservers of controllability and/or observability
• Linear preserver problems and algebraic groups
• Introduction to model theory and to the metamathematics of algebra
• Linear Transformations Preserving Potent Matrices
• Pairs of Matrices With Property L. II
• The maximal subgroups of the classical groups
• Linear Transformations on Algebras of Matrices: The Invariance of the Elementary Symmetric Functions
• Mathematical Aspects of the Relative Gain Array $( A \circ A^{ - T} )$
• Spaces of matrices of fixed rank
• Linear transformations preserving the unitary group
• Linear maps preserving regional eigenvalue location
• Rigid Embedding of Simple Groups in the General Linear Group
• On a certain functional identity in prime rings^*
• Mappings which Preserve Idempotents, Local Automorphisms, and Local Derivations
• Linear Operators Preserving Similarity Classes and Related Results
• Invertible Preservers and Algebraic Groups II: Preservers of Similarity Invariants and Overgroups ofPSL_n(F)
• Linear Operators Preserving Certain Equivalence Relations on Matrices
• Jordan Homomorphisms of Rings
• On the automorphisms of the classical groups. With a supplement by Loo-Keng Hua
• Pairs of Matrices with Property L
• Linear operators on matrices: The invariance of rank-k matrices
• Preserving commutativity