Refinements of Kantorovich type, Schwarz and Berezin number inequalities

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.

Keywords

• Reproducing kernel Hilbert space
• Berezin symbol
• Berezin number
• Kantorovich type inequality
• C∗ -module