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 $A,B, C\in \mathcal{B}(\mathcal{H}).$

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有界线性算子的 Davis-Wielandt 半径的界限

我们获得了在复杂 Hilbert 空间上定义的有界线性算子的 Davis-Wielandt 半径的上限和下限，这对现有的进行了改进。我们还获得了算子矩阵的 Davis-Wielandt 半径的界限。我们确定两种特殊类型的算子矩阵 $\left(\begin{array}{cc} I & B 0 & 0 \end{array}\right)$ 和 $\left( \begin{array}{cc} 0 & AB & 0 \end{array}\right)$，其中 $A,B\in \mathcal{B}(\mathcal{H})$、$I$ 和 $0$分别是 $\mathcal{H},$ 上的恒等运算符和零运算符。最后，我们获得了 $\left(\begin{array}{cc} A& B 0 & C \end{array}\right),$ 形式的算子矩阵的 Davis-Wielandt 半径的边界，其中 $A,B, C \in \mathcal{B}(\mathcal{H}).$