Further inequalities for the Α-numerical radius of certain 2 x 2 operator matrices

Let Alpha = ( A O (O A)) be a 2 x 2 diagonal operator matrix whose each diagonal entry is a bounded positive (semi-definite) linear operator A acting on a complex Hilbert space H. In this paper, we derive several Alpha-numerical radius inequalities for 2 x 2 operator matrices whose entries are bounded with respect to the seminorm induced by the positive operator A on H. Some applications of our inequalities are also given.