Improvement of A-Numerical Radius Inequalities of Semi-Hilbertian Space Operators

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