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 H which are bounded with respect to the semi-norm induced by a positive operator A on 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 A-numerical radius inequalities of operator matrices where A is the operator diagonal matrix with diagonal entries are positive operator A. Some other related results are also investigated.

Further inequalities for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices

“…In addition, for T ∈ B A (H), we have (T ♯ A ) ♯ A = P R(A) T P R(A) = T . For further details about A-numerical radius, interested readers can follow [5,6,7,12,21,18] and the references therein.…”

$A$-numerical radius : New inequalities and characterization of equalities

“…More refinements in this direction are also given in [3,4,5,6,7,13,14]. Inspired by the inequalities obtained in the article [8,9], here we obtain new refinements of the first inequalities in (1.1) and (1.2).…”

Some bounds for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices

“…for every A-unitary operator U ∈ B A (H) and T ∈ B A 1/2 (H) (see [5,Lemma 3.8]). For the sequel, for any arbitrary operator T ∈ B A (H), we denote…”