Refinements of q-Berezin radius inequalities

Abstract

We present refinements of q-Berezin radius inequalities for bounded linear operators on repro- ducing kernel Hilbert spaces. Using the Berezin number, the Berezin–Crawford number, the Berezin norm, and the quantity ˜m(P), we derive upper bounds whose coefficient functions remain bounded on [0, 1]. One of these bounds is no larger than an earlier adapted estimate for every admissible value of q, while the estimate involving ˜m(P) may be sharper under an explicit condition. We also obtain inequalities for products of operators, including an appli- cation of Buzano’s inequality. Concrete examples demonstrate both the improvement over previously adapted estimates and the sharpness of certain RKHS-adapted linear inequalities.