On A-numerical radius inequalities for $2\times 2$ operator matrices

Let ($\mathcal{H},⟨\mathrm{.},\mathrm{.}⟩)$ be a complex Hilbert space and $A$ be a positive bounded linear operator on it. Let $w_A(T)$ be the $A$-numerical radius and $\mathrm{\parallel }T{\mathrm{\parallel }}_A$ be the $A$-operator seminorm of an operator $T$ acting on the semi-Hilbertian space $(\mathcal{H},⟨\mathrm{.},\mathrm{.}{⟩}_A),$ where $\langle x, y\rangle_A:=\langle Ax, y\rangle$forall$x,y\in $\mathcal{H}$$. In this article, we establish several upper and lower bounds for $B$-numerical radius of $2\times 2$ operator matrices, where $B=\begin{bmatrix} A & 0 0 & A \end{bmatrix}$\mathrm{.}Further,weprovesomerefinementsofearlier$A$-numerical radius inequalities for operators.