Abstract
In this paper, by using some classical operator means and classical operator inequalities, we investigate Berezin number of operators. In particular, we compare the Berezin number of some operator means of two positive operators. We also use some Hardy type inequalities to obtain a power inequality for the Berezin number of an operator. Moreover, by applying some inequalities for nonnegative Hermitian forms, some vector inequalities for n-tuple operators via Berezin symbols are established.