Improved upper bounds for the Berezin numbers of operators on reproducing kernel Hilbert spaces

In this article, several upper bounds for the Berezin numbers of bounded linear operators on reproducing kernel Hilbert spaces are obtained through the use of interpolation paths of symmetric means and Orlicz functions.

With suitable selections of these paths and functions, we show that the results presented here refine and generalize several earlier known findings.

Furthermore, we derive some Berezin number inequalities for such operators using refined Young's inequalities.