$$\mathbb {A}$$ -Berezin Number Inequalities for $$2\times 2$$ Operator Matrices

Abstract

Let \(\mathbb {A}\) be the \(2\times 2\) diagonal operator matrix determined by a positive Hilbert space operator A. We give several upper bounds for the \(\mathbb {A}\)-Berezin number of \(2\times 2\) block matrices on a reproducing kernel Hilbert space and prove inequalities for the A-Berezin number of Hilbert space operators. Our results in this paper generalize and refine earlier the A-Berezin number inequalities.