On q-Berezin number inequalities in reproducing kernel Hilbert space

Abstract

This work focuses on the classical Berezin number and the q-Berezin number of bounded linear operators on a reproducing kernel Hilbert space. In this study, we also present the q-Berezin transform, the q-Berezin interval, and the q-Berezin number of the reproducing kernel Hilbert space, as well as show various q-Berezin number inequalities that generalize prior inequalities provided with the standard Berezin number. Some other connected questions are also addressed.