Further inequalities for the 𝔸-numerical radius of certain 2 × 2 operator matrices

Let 𝔸=(AOOA)\mathbb{A}={\bigl{(}\begin{smallmatrix}A&O\\ O&A\\ \end{smallmatrix}\bigr{)}}be a 2×22\times 2diagonal operator matrix whose each diagonal entry is a bounded positive (semi-definite) linear operator Aacting on a complex Hilbert space ℋ\mathcal{H}. In this paper, we derive several 𝔸\mathbb{A}-numerical radius inequalities for 2×22\times 2operator matrices whose entries are bounded with respect to the seminorm induced by the positive operator Aon ℋ\mathcal{H}. Some applications of our inequalities are also given.