Birkhoff-James orthogonality and applications: a survey
From MaRDI portal
Publication:1980919
DOI10.1007/978-3-030-51945-2_15zbMath1482.46017arXiv2005.07399OpenAlexW3185496673MaRDI QIDQ1980919
Priyanka Grover, Sushil Singla
Publication date: 9 September 2021
Full work available at URL: https://arxiv.org/abs/2005.07399
orthogonalitysmooth pointGâteaux differentiabilityBirkhoff-James orthogonalitysubdifferential setcyclic representationnorm-parallelism\(C^\ast \)-algebrafaces of unit ball
Best approximation, Chebyshev systems (41A50) Geometry and structure of normed linear spaces (46B20) (C^*)-modules (46L08) Commutators, derivations, elementary operators, etc. (47B47) General theory of (C^*)-algebras (46L05) Research exposition (monographs, survey articles) pertaining to functional analysis (46-02)
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A nonlinear characterization of type I factors based on strong Birkhoff-James orthogonality, Birkhoff–James Orthogonality: Characterizations, Preservers, and Orthogonality Graphs, Orthonormal pairs of operators, A distance formula for tuples of operators, Nonlinear Birkhoff-James orthogonality preservers in smooth normed spaces, Subdifferential set of the joint numerical radius of a tuple of matrices, Birkhoff-James orthogonality in certain tensor products of Banach spaces, Gateaux derivative of \(C^\ast\) norm, Symmetrized Birkhoff-James orthogonality in arbitrary normed spaces
Cites Work
- Orthogonality and Linear Functionals in Normed Linear Spaces
- Inner products in normed linear spaces
- Modules Over Operator Algebras
- Orthogonality of matrices
- Orthogonality of matrices
- Orthogonality in normed linear spaces
- Orthogonality in \({\mathcal C}_p\) classes
- Range-kernel orthogonality of the elementary operator \(X\to\sum_{i=1}^n A_iXB_i - X\)
- Generalized Anderson's inequality
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The operator-valued parallelism
- A strong version of the Birkhoff-James orthogonality in Hilbert \(C^\ast\)-modules
- Leibniz seminorms and best approximation from \(C^*\)-subalgebras
- The Birkhoff-James orthogonality in Hilbert \(C^{\ast }\)-modules
- Smooth points in spaces of operators
- Gâteaux derivative of the norm in \(\mathcal{K}(X;Y)\)
- Birkhoff-James orthogonality and smoothness of bounded linear operators
- On symmetry of the (strong) Birkhoff-James orthogonality in Hilbert \(C^*\)-modules
- The space of completely continuous operators on a Hilbert space
- On some norm equalities in pre-Hilbert \(C^{\ast}\)-modules
- Variance bounds, with an application to norm bounds for commutators
- Rank one operators and norm of elementary operators
- Norm-parallelism in the geometry of Hilbert \(C^\ast\)-modules
- Smooth points of some operator spaces
- On the characterization of the extremal points of the unit sphere of matrices
- Operators that are orthogonal to the range of a derivation
- On the geometry of the unit ball of unitary matrix spaces
- Smooth points of certain operator spaces
- Characterization of the subdifferential of some matrix norms
- Smooth points in some spaces of bounded operators
- Geometry of Banach spaces. Selected topics
- The differentiability of the norm in spaces of operators
- Norm derivatives on spaces of operators
- Orthogonality of matrices and some distance problems
- On matrix approximation problems with Ky Fan \(k\) norms
- Very smooth points of spaces of operators
- Some versions of Anderson's and Maher's inequalities. I
- Some versions of Anderson's and Maher's inequalities. II
- Elementary operators and orthogonality.
- On symmetry of Birkhoff-James orthogonality of linear operators
- Symmetry of Birkhoff-James orthogonality of operators defined between infinite dimensional Banach spaces
- On some geometric properties of operator spaces
- Linear mappings approximately preserving orthogonality
- Characterizations of inner product spaces
- Characterization of Birkhoff-James orthogonality
- Approximate Birkhoff-James orthogonality and smoothness in the space of bounded linear operators
- Operator norm attainment and Birkhoff-James orthogonality
- Subdifferentials, faces, and dual matrices
- Smooth points and M-ideals
- Norm-parallelism in classical \(M\)-ideals
- Approximate orthogonality in normed spaces and its applications
- Orthogonality of compact operators
- A remark on orthogonality and symmetry of operators in \(\mathcal{B}(\mathcal{H})\)
- Characterizations of norm-parallelism in spaces of continuous functions
- Operator norm attainment and inner product spaces
- Standard deviation is a strongly Leibniz seminorm
- Orthogonality to matrix subspaces, and a distance formula
- Derivations of operator algebras
- Derivations of \(W^ *\)-algebras
- Derivations on \(B^*\) algebras
- The norm of a derivation
- On the metric geometry of ideals of operators on Hilbert space
- On operators preserving James' orthogonality
- Operator algebras. Theory of \(C^*\)-algebras and von Neumann algebras
- Orthogonality in linear metric spaces
- Orthogonality of matrices in the Ky Fan k-norms
- Facial structures of schattenp-Norms
- On the injective norm of ∑_i=1^n A_i ∑ B_i and characterization of normaloid operators
- On normal derivations of Hilbert–Schmidt type
- Smooth, Compact Operators
- Commutator Approximants
- On the range and the kernel of the operator 𝑋\mapsto𝐴𝑋𝐵-𝑋
- A remark on normal derivations
- Orthogonality of the range and the kernel of some elementary operators
- On symmetry of Birkhoff-James orthogonality of linear operators on finite-dimensional real Banach spaces
- A complete characterization of Birkhoff-James orthogonality in infinite dimensional normed space
- Orthogonality in Generalized Minkowski Spaces
- On approximate Birkhoff-James orthogonality and normal cones in a normed space
- Adjoints of operators as smooth points in spaces of compact operators
- Gateaux derivative of 𝐵(𝐻) norm
- Normal Derivations in Norm Ideals
- Another Generalization of Anderson's Theorem
- Exact and Approximate Operator Parallelism
- On three concepts of orthogonality in HilbertC*-modules
- Best approximations, distance formulas and orthogonality in C*-algebras
- A complete characterization of smoothness in the space of bounded linear operators
- Norm-parallelism and the Davis–Wielandt radius of Hilbert space operators
- Finite Operators
- Norm of a Derivation on a Von Neumann Algebra
- On Normal Derivations
- The Norm of a Derivation in a W ∗ -Algebra
