$A$-Numerical radius orthogonality and parallelism of semi-Hilbertian space operators and their applications

Abstract

In this paper, we aim to introduce and characterize the concept of numerical radius orthogonality of operators on a complex Hilbert space $\mathcal{H}$ which are bounded with respect to the semi-norm induced by a positive operator $A$ on $\mathcal{H}$. Moreover, a characterization of the $A$-numerical radius parallelism for $A$-rank one operators is proved. As applications of the obtained results, we obtain some $\mathbb{A}$-numerical radius inequalities of operator matrices where $\mathbb{A}$ is the operator diagonal matrix with diagonal entries are positive operator $A$. Some other related results are also investigated.

References in corpus (5)

• Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces
• Numerical radius inequalities and its applications in estimation of zeros of polynomials
• Refinements of A-numerical radius inequalities and their applications
• Numerical radius inequalities of operator matrices with applications
• Some improvements of numerical radius inequalities of operators and operator matrices

Cited by in corpus (5)

• Some numerical radius inequalities for semi-Hilbert space operators
• Refinement of seminorm and numerical radius inequalities of semi-Hilbertian space operators
• Further inequalities for the $\mathbb{A}$-numerical radius of certain $2\times 2$ operator matrices
• $A$-numerical radius : New inequalities and characterization of equalities
• Improvement of $A$-numerical radius inequalities of semi-Hilbertian space operators