论文标题
$ 2 \ times 2 $操作员矩阵上的数字半径不平等现象
On A-numerical radius inequalities for $2 \times 2$ operator matrices
论文作者
论文摘要
让（$ \ nathcal {h}，\ langle。，。\ rangle）$是一个复杂的希尔伯特空间，$ a $为正面有限的线性运算符。令$ w_a（t）$为$ a $ numerical半径，$ \ | t \ | _a $是$ a $ a $ a $ - 操作员$ t $ a $ t $作用于semi-hilbertian space $（\ nathcal {h}，h}，\ langle。 y \ rangle_a：= \ langle ax，y \ rangle $ for hast $ x，y \ in \ mathcal {h} $。在本文中，我们为$ b $ numerical radius建立了几个上限和下限，为$ 2 \ times 2 $运算符矩阵，其中$ b = \ begin {bmatrix} A＆0 0＆a \ end {bmatrix} $。此外，我们证明了对运营商的早期$ numerical半径不平等的一些改进。
Let ($\mathcal{H}, \langle . , .\rangle )$ be a complex Hilbert space and $A$ be a positive bounded linear operator on it. Let $w_A(T)$ be the $A$-numerical radius and $\|T\|_A$ be the $A$-operator seminorm of an operator $T$ acting on the semi-Hilbertian space $(\mathcal{H}, \langle .,.\rangle_A),$ where $\langle x, y\rangle_A:=\langle Ax, y\rangle$ for all $x,y\in \mathcal{H}$. In this article, we establish several upper and lower bounds for $B$-numerical radius of $2\times 2$ operator matrices, where $B=\begin{bmatrix} A & 0 0 & A \end{bmatrix}$. Further, we prove some refinements of earlier $A$-numerical radius inequalities for operators.
