Orthogonality and Numerical radius inequalities of operator matrices

Abstract

We completely characterize Birkhoff-James orthogonality with respect to numerical radius norm in the space of bounded linear operators on a complex Hilbert space. As applications of the results obtained, we estimate lower bounds of numerical radius for n × n operator matrices, which improve on and generalize existing lower bounds. We also obtain a better lower bound of numerical radius for an upper triangular operator matrix.

A-Numerical Radius Orthogonality and Parallelism of Semi-Hilbertian Space Operators and Their Applications

“…In addition, a characterization of the A-numerical radius parallelism of A-rank one operators is established. Our results cover and extend the works in [16,18]. In the last section, we give some inequalities for A-numerical radius of semi-Hilbertian space operators which are as an application of A-numerical radius orthogonality and parallelism.…”

“…Remark 2.4. In general, as it was point out in [16] that the above two notions of orthogonality are not equivalent.…”

Numerical radius orthogonality in $$C^*$$-algebras

“…In the following result we characterize a positive-real version of the numerical radius Birkhoff-James orthogonality. Our approach is similar to the one given in [11]. Proof.…”

“…Very recently, the numerical radius Birkhoff-James orthogonality in B(H ) has been studied in [11] as our work was in progress. In fact, Mal et In what follows we shall develop the above result for elements of a C * -algebra.…”

Birkhoff-James orthogonality to a subspace of operators defined between Banach spaces

“…Now, considering different states on L(H), we obtain lower bounds for distance of an operator T from Span{A}, using Equation 1. For example, suppose that In [11], the authors obtained characterization of "numerical radius orthogonality (⊥ w )", i.e., Birkhoff-James orthogonality in L(H) with respect to numerical radius norm. Here we obtain a sufficient condition for numerical radius orthogonality of an operator in L(H) to a subspace of L(H).…”