论文标题
限制线性操作员的戴维斯 - 韦兰特半径的界限
Bounds for the Davis-Wielandt radius of bounded linear operators
论文作者
论文摘要
我们获得了在复杂的希尔伯特空间上定义的有限线性算子的戴维斯 - 韦兰特半径的上限和下限，该线性算子对现有空间有所改善。我们还获得了操作员矩阵半径的界限。我们确定两种特殊类型的操作员矩阵$ \ left的davis-wielandt半径的确切值（\ begin {array} {cc} i＆b 0＆0 \ end {array} \ right）$和$ \ left（\ begin {array} {cc} 0＆a B＆0 \ end {array} \ right）$，其中$ a，b \ in \ mathcal {b}（\ Mathcal {h}）$，$ i $和$ 0 $是$ \ MATHCAL {H}，$的身份操作员和零操作员。最后，我们获得了$ \ left的运算符矩阵的davis-wielandt半径的界限（\ begin {array} {cc} A＆B 0＆c \ end {array} \ right），其中$ a，b，c \ in \ mathcal {b}（\ mathcal {h}）。$
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 $A,B, C\in \mathcal{B}(\mathcal{H}).$
