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 an upper bound for the \(\mathbb {A}\)-operator seminorm of \(2\times 2\) operator matrices, where \(\mathbb {A}=\text{ diag }(A,A)\). The bound obtained here generalizes the earlier related bound.