In this paper, we generalize several inequalities involving powers of the Davis-Wielandt radius for off-diagonal part of $2\times 2$ operator matrices of the form $T=\left(\begin{array}{cc}0& B\\ C& 0\end{array}\right)$, where B and C are two bounded linear operators. We also obtain some new upper and lower bounds for the Davis-Wielandt radius of bounded linear operators, which generalize the existing ones.

中文翻译：

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非对角算子矩阵的戴维斯-维兰特半径不等式

在本文中，我们概括了几个涉及 Davis-Wielandt 半径的幂的不等式，用于非对角线部分$\mathrm{2个}\times \mathrm{2个}$形式的运算符矩阵$吨=\left(\begin{array}{cc}0& 乙\\ C& 0\end{array}\right)$，其中B和C是两个有界线性算子。我们还得到了有界线性算子的戴维斯-维兰特半径的一些新的上下界，它们推广了现有的。