Abstract
In this article, the concept of the A-Davis-Wielandt Berezin number is introduced for positive operatorA. Some upper and lower bounds for the A-Davis-Wielandt Berezin number are proved. Moreover, some inequalities related to the concept of the Davis-Wielandt Berezin number are obtained, which are generalizations of known results. Among them, it is shown that ber2 dw(S) ? inf ??C {(2||Re(?)Re(S) + Im(?)Im(S)|| + ||S*S ? 2Re(??S)2|| + 2||Re(??S)|| ? |?|2 + ber2(S ? ?I)}, where S ? B(H(?)). Also, we determined the exact value of the A-Davis-Wielandt Berezin number of some special type of operator matrices.
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