论文标题
关于半希尔伯特太空运营商的广义戴维斯 - 韦兰特半径不平等
On generalized Davis-Wielandt radius inequalities of semi-Hilbertian space operators
论文作者
论文摘要
让$ a $为复杂的希尔伯特空间上的正（半芬派）运算符$ \ mathcal {h} $，让$ \ mathbb {a} = \ left（\ begin {arnay} {cc} {cc} A＆O O＆A \ end {array} \ right）。$我们获得了$ a $ -davis-wielandt半径的半希尔伯特空间操作员的上限和下限，这些半径是对现有$ -Davis-Wielandt Radius的概括和改进。我们还获得了$ \ mathbb {a} $ - davis-wielandt半径为$ 2 \ times 2 $运算符矩阵的上限。最后，我们确定两个操作员矩阵$ \ left的$ \ mathbb {a} $ - davis-wielandt半径（\ begin {array} {cc} {cc} i＆x \\ 0＆x \\ 0＆0＆0 \ end {array {array} \ right） \ end {array} \ right）$，其中$ x $是半希尔伯特空间操作员。
Let $A$ be a positive (semidefinite) operator on a complex Hilbert space $\mathcal{H}$ and let $\mathbb{A}=\left(\begin{array}{cc} A & O O & A \end{array}\right).$ We obtain upper and lower bounds for the $A$-Davis-Wielandt radius of semi-Hilbertian space operators, which generalize and improve on the existing ones. We also obtain upper bounds for the $\mathbb{A}$-Davis-Wielandt radius of $2 \times 2$ operator matrices. Finally, we determine the exact value for the $\mathbb{A}$-Davis-Wielandt radius of two operator matrices $\left(\begin{array}{cc} I & X\\ 0 & 0 \end{array}\right)$ and $\left(\begin{array}{cc} 0 & X\\ 0 & 0 \end{array}\right)$, where $X $ is a semi-Hilbertian space operator.
