Abstract
Let A be a bounded linear positive operator on a complex Hilbert space {mathcal {H}}. Furthermore, let {mathcal {B}}_Amathcal {(H)} denote the set of all bounded linear operators on {mathcal {H}} whose A-adjoint exists, and {mathbb {A}} signify a diagonal operator matrix with diagonal entries are A. Very recently, several {mathbb {A}}-numerical radius inequalities of 2times 2 operator matrices were established. In this paper, we prove a few new {mathbb {A}}-numerical radius inequalities for 2times 2 and ntimes 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.
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