Birkhoff-James orthogonality and applications : A survey
arXiv:2005.07399 · doi:10.1007/978-3-030-51945-2_15
Abstract
In the last few decades, the concept of Birkhoff-James orthogonality has been used in several applications. In this survey article, the results known on the necessary and sufficient conditions for Birkhoff-James orthogonality in certain Banach spaces are mentioned. Their applications in studying the geometry of normed spaces are given. The connections between this concept of orthogonality, and the Gateaux derivative and the subdifferential set of the norm function are provided. Several interesting distance formulas can be obtained using the characterizations of Birkhoff-James orthogonality, which are also mentioned. In the end, some new results are obtained.
arXiv commentIn Equation (4.1), the factor of 2 is misplaced and it should be on the left-hand side of the equation
References in corpus (11)
- Birkhoff-James orthogonality and smoothness of bounded linear operators
- Norm-parallelism in the geometry of Hilbert -modules
- A complete characterization of smoothness in the space of bounded linear operators
- Exact and approximate operator parallelism
- Leibniz Seminorms and Best Approximation from C*-subalgebras
- On Symmetry of Birkhoff-James Orthogonality of Linear Operators on Finite-dimensional Real Banach Spaces
- On some geometric properties of operator spaces
- Norm-parallelism and the Davis--Wielandt radius of Hilbert space operators
- Orthogonality of matrices in the Ky Fan -norms
- Symmetry of Birkhoff-James orthogonality of operators defined between infinite dimensional Banach spaces
- Best approximations, distance formulas and orthogonality in C*-algebras