Čebyšev's type inequalities and power inequalities for operators of Berezin number

Abstract

We give operator analogues of some classical inequalities, including Čebyšev type inequality for synchronous and convex functions of selfadjoint operators in Reproducing Kernel Hilbert Spaces (RKHSs). We obtain some Berezin number inequalities for the product of operators. Also, we prove the Berezin number inequality for the commutator of two operators.