Further results on A-numerical radius inequalities

Let A be a bounded linear positive operator on a complex Hilbert space H. Furthermore, let B-A double left arrow H double right arrow denote the set of all bounded linear operators on H whose A-adjoint exists, and A signify a diagonal operator matrix with diagonal entries are A. Very recently, several A-numerical radius inequalities of 2 x 2 operator matrices were established. In this paper, we prove a few new A-numerical radius inequalities for 2 x 2 and n x n operator matrices. We also provide a new proof of an existing result by relaxing a sufficient condition "A is strictly positive". Our proofs show the importance of the theory of the Moore-Penrose inverse of a bounded linear operator in this field of study.