Berezin number of operators and related questions - Karaev, M. T.; Iskenderov, N. Sh. (Methods of Functional Analysis and Topology, 2013)
We prove some estimates for the Berezin number of operators on the reproducing kernel Hilbert spaces. We also give in terms of Berezin number necessary and sufficient conditions providing unitarity of invertible operator on the reproducing kernel Hilbert space. Moreover, we give a lower estimate for any operator on the Hardy space H^2( D ) over the unit disc D.