Orthogonality of matrices in the Ky Fan k-norms

Abstract

We obtain necessary and sufficient conditions for a matrix A to be Birkhoff-James orthogonal to another matrix B in the Ky Fan knorms. A characterization for A to be Birkhoff-James orthogonal to any subspace W of M(n) is also obtained. ARTICLE HISTORY

Orthogonality and Numerical radius inequalities of operator matrices

“…In a Banach space X, Birkhoff-James orthogonality is defined in the following way. For x, y ∈ X, x is said to be Birkhoff-James orthogonal to y, written as x ⊥ B y, if x + λy ≥ x for all λ ∈ K. Recently, many authors have studied orthogonality on B(H) with respect to different norms [5,6,13,14,15]. Motivated by these, we study "numerical radius orthogonality" on B(H).…”

Numerical Radius Parallelism of Hilbert Space Operators

“…Some characterizations of the norm-parallelism for operators on various Banach spaces and elements of an arbitrary Hilbert C * -module were given in [1,3,9,11,13,14,15]. and so T ω I.…”

Orthogonality and Parallelism of Operators on Various Banach Spaces

“…Also, for matrices, Bhatia andŠemrl [5] obtained a generalization of Kittaneh's result and other statements concerning the spectral norm. More recently, some other authors studied different aspects of orthogonality of bounded linear operators and elements of an arbitrary Hilbert C *module; for instance, see [4,6,12,15,26,27,29,33,34].…”

“…x y ⇔ x ⊥ BJ ( y x + λ x y) for some λ ∈ T . (1.4) Some characterizations of the norm-parallelism for Hilbert space operators and elements of an arbitrary Hilbert C * -module were given in [15,[35][36][37][38].…”