Improvement of $A$-numerical radius inequalities of semi-Hilbertian space operators

Abstract

Let $\mathcal{H}$ be a complex Hilbert space and let $A$ be a positive operator on $\mathcal{H}$. We obtain new bounds for the $A$-numerical radius of operators in semi-Hilbertian space ${\mathcal{B}}_A(\mathcal{H})$ that generalize and improve on the existing ones. Further, we estimate bounds for the $B$-operator seminorm and $B$-numerical radius of $2\times 2$ operator matrices, where $B=\mbox{diag}(A,A)$. The bounds obtained here improve on the existing ones.

References in corpus (3)

• Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces
• $A$-Numerical radius orthogonality and parallelism of semi-Hilbertian space operators and their applications
• Refinements of A-numerical radius inequalities and their applications