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

Abstract

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