FURTHER REFINEMENTS OF DAVIS-WIELANDT RADIUS INEQUALITIES

Suppose T,S are bounded linear operators on a complex Hilbert space. We show that the Davis-Wielandt radius dw(center dot) satisfies the following inequalities dw(T + S) <= root 2(dw(2)(T) + dw(2)(S)) + 6 parallel to |T|(4) +|S|(4) parallel to <= 2 root 2 root dw(2)(T) + dw(2)(S) <= 2 root 2(dw(T) + dw(S)). From the third inequality we obtain the following lower and upper bounds for the Davis-Wielandt radius dw(T) of the operator T : dw(T) >= 1/4 root 2 max {dw(2Re(T)),dw(2Im(T))}, dw(T) <= 2 root 2(dw(Re(T)) + dw(Im(T))). Further, we develop several new lower and upper bounds for the Davis-Wielandt radius of the operator T which improve the existing ones. Application of these bounds are also provided.