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

Abstract

In this paper, we aim to introduce and characterize the numerical radius orthogonality of operators on a complex Hilbert space $${\mathcal {H}}$$ which are bounded with respect to the seminorm induced by a positive operator A on $${\mathcal {H}}$$ . Moreover, a characterization of the A-numerical radius parallelism for A-rank one operators is obtained. As applications of the results obtained, we derive some $${\mathbb {A}}$$ -numerical radius inequalities of operator matrices, where $${\mathbb {A}}$$ is the operator diagonal matrix whose each diagonal entry is a positive operator A on a complex Hilbert space $${\mathcal {H}}.$$