JOURNAL OF MATHEMATICAL INEQUALITIES, vol.13, no.4, pp.1117-1128, 2019 (Journal Indexed in SCI)
In this paper, several refinements of the Berezin number inequalities are obtained. We generalize inequalities involving powers of the Berezin number for product of two operators acting on a reproducing kernel Hilbert space H = H(Omega) and also impmve them. Among other inequalities, it is shown that if A,B is an element of B(H) such that vertical bar A vertical bar B = B* vertical bar A vertical bar. f and g are nonnegative continuous functions on [0,infinity) satisfying f(t)g(t) = t (t >= 0). then