Abstract
In this article, we use Kantorovich and Kantorovich type inequalities in order to prove some new Berezin number inequalities. Also, by using a refinement of the classical Schwarz inequality, we prove Berezin number inequalities for powers of f (A), where A is self-adjoint operator on the Hardy space H 2(D) and f is a positive continuous function. Some related questions are also discussed.
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