On inequalities for A-numerical radius of operators

Abstract

Let $A$ be a positive operator on a complex Hilbert space $\mathcal{H}.$ Inequalities are presented concerning upper and lower bounds for $A$-numerical radius of operators, which improve on and generalize the existing ones, studied recently in [A. Zamani. A-Numerical radius inequalities for semi-Hilbertian space operators. Linear Algebra Appl., 578:159--183, 2019]. Also, some inequalities are obtained for $B$-numerical radius of $2\times 2$ operator matrices, where $B$ is the $2\times 2$ diagonal operator matrix whose diagonal entries are $A$. Further, upper bounds are obtained for $A$-numerical radius for product of operators, which improve on the existing bounds.