A-DAVIS-WIELANDT-BEREZIN RADIUS INEQUALITIES

We consider operator V on the reproducing kernel Hilbert space 7-l = 7-l (ohm) over some set ohm with the reproducing kernel KH,lambda (z) = K (z, lambda) and define A-Davis-Wielandt-Berezin radius eta A (V ) by the formula [GRAPHICS] and V is the Berezin symbol of V where any positive operator A-induces a semi-inner product on 7-l is defined by (x, y)A = (Ax, y) for x, y E 7-l. We study equality of the lower bounds for A-Davis-Wielandt-Berezin radius mentioned above. We establish some lower and upper bounds for the A-Davis-Wielandt-Berezin radius of reproducing kernel Hilbert space operators. In addition, we get an upper bound for the A-Davis-Wielandt-Berezin radius of sum of two bounded linear operators.