New Inequalities for Davis-Wielandt Radius of Hilbert Space Operators

Let T be a bounded linear operator on a complex Hilbert space and dw(T) denote the Davis-Wielandt radius of the operator T. We prove that dw(2) (T) <= min(0 <=alpha <= 1) parallel to alpha|T|(2) + (1 - alpha)|T *|(2) + |T|(4) and dw(2) (T) <= min(0 <=alpha <= 1) parallel to alpha|T|(2) + (1 - alpha)|T *|(2) + |T*|(4), where |T| = root T*T, |T *| = root TT*. We also develop several other bounds for the Davis-Wielandt radius and prove that the bounds obtained here are better than the existing ones.