Refined q-Berezin Radius Inequalities for Operators and 2×2 Block Matrices

Abstract

In this paper, we establish upper bounds for the q-Berezin radii of bounded linear operators acting on reproducing kernel Hilbert spaces. Specifically, we derive inequalities for the sum X+Y and product Y∗X of operators utilizing the Berezin norms of operator powers and integral refinements of the Cauchy-Schwarz inequality. We further provide explicit estimates for the q-Berezin radii of 2×2 block operator matrices bounding the off-diagonal terms in relation to the diagonal entries. The obtained results recover the standard Berezin number inequalities when q=1 and provide stronger estimates than the existing upper bounds for the general q-numerical radius.