On $\mathbb{A}$-numerical radius inequalities for $2 \times2$ operator matrices-II

Abstract

Rout et al.[Linear Multilinear Algebra 2020, DOI: 10.1080/03081087.2020.1810201] presented some $\mathbb{A}$-numerical radius inequalities for $2\times 2$ operator matrices and further results on $\mathbb{A}$-numerical radius of certain $2\times 2$ operator matrices are obtained by Feki [Hacet. J. Math. Stat., 2020 to appear], very recently. The main goal of this article is to establish several new upper and lower bounds for the $\mathbb{A}$-numerical radius of $2\times 2$ operator matrices, where $\mathbb{A}$ be the $2\times 2$ diagonal operator matrix whose diagonal entries are positive bounded operator $A$. Certain $\mathbb{A}$-numerical radius equalities for operator matrices are also proved. Further, we prove some refinements of earlier $A$-numerical radius inequalities for operators. Finally, we present an application of our result.