Bounds for the Davis-Wielandt radius of bounded linear operators

We obtain upper and lower bounds for the Davis-Wielandt radius of bounded linear operators defined on a complex Hilbert space, which improve on the existing ones. We also obtain bounds for the Davis-Wielandt radius of operator matrices. We determine the exact value of the Davis-Wielandt radius of two special type of operator matrices $\left(\begin{array}{cc} I & B 0 & 0 \end{array}\right)$and$\left(\begin{array}{cc} 0 & A B & 0 \end{array}\right)$,where$A,B\in $\mathcal{B}$($\mathcal{H}$)$,$I$and$0$ are the identity operator and the zero operator on $\mathcal{H},$ respectively. Finally we obtain bounds for the Davis-Wielandt radius of operator matrices of the form $\left(\begin{array}{cc} A& B 0 & C \end{array}\right),$where$A,B, C\in $\mathcal{B}$($\mathcal{H}$).$