Further q-Berezin Radius Inequalities on Reproducing Kernel Hilbert Spaces

Abstract

We develop several new inequalities for the q-Berezin radii of bounded linear operators on reproducing kernel Hilbert spaces. Our first purpose is to provide a corrected and fully rigorous proof of a previously stated estimate for the q-Berezin radii of operator sums. Building on that correction, we then establish product-type estimates for operators of the form AαXBβ, prove a Heinz-type inequality in the q-Berezin setting, and derive a lower bound for the q-Berezin radius in terms of the Berezin norm of T∗T+TT∗. These results sharpen and extend earlier estimates in the literature, while highlighting the geometric role played by the parameter q and the reproducing-kernel structure of the underlying Hilbert space.