On Berezin norm and Berezin number inequalities for sum of operators

The aim of this study is to obtain several inequalities involving the Berezin number and the Berezin norm for various combinations of operators acting on a reproducing kernel Hilbert space. First, we present some bounds regarding the Berezin number associated with W*Q+W*Q′{W}^{* }Q+{W}^{* }Q^{\prime} , where WW, QQ, and Q′Q^{\prime} are three bounded linear operators. Next, several Berezin norm and Berezin number inequalities for the sum of nn operators are established.