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

Let XN = (X (N) 1 , . . . , X (N) p ) be a family of N × N independent, normalized random matrices from the Gaussian Unitary Ensemble. We state sufficient conditions on matrices YN = (Y (N) 1 , . . . , Y (N) q ), possibly random but independent of XN , for which the operator norm of P (XN ,YN ,Y∗ N) converges almost surely for all polynomials P . Limits are described by operator norms of object...