Refinements of some inequalities involving Berezin norms and Berezin number and related questions

Abstract

In this paper, we give several refinements of Berezin norm and Berezin number inequalities of bounded linear operators defined on a reproducing kernel Hilbert space. In particular, we present some refinements of the triangle inequality for the Berezin norm of operators. In addition, we derive new upper bounds for the sum and poduct of Berezin number for two bounded operators. Moreover, we prove some new upper bounds for the Davis–Wielandt–Berezin radius of operators. Some applications of the newly obtained inequalities are also provided.