Davis-Wielandt-Berezin radius inequalities of Reproducing kernel Hilbert space operators

Abstract

Several upper and lower bounds of the Davis-Wielandt-Berezin radius of bounded linear operators defined on a reproducing kernel Hilbert space are given. Further, an inequality involving the Berezin number and the Davis-Wielandt-Berezin radius for the sum of two bounded linear operators is obtained, namely, if A and B are reproducing kernel Hilbert space operators, then η(A + B) ≤ η(A) + η(B) + ber(A * B + B * A), where η(•) and ber(•) are the Davis-Wielandt-Berezin radius and the Berezin number, respectively.