论文标题
关于块对角线运算符基本数值范围的注释
A note on the essential numerical range of block diagonal operators
论文作者
论文摘要
在本说明中，我们表征了块对角线O \ -pe \ -pe \ -ra \ -tor $ t = \ bigoplus_i t_i $的基本数值范围。具体而言，$ t $的基本数值范围是$ \ {w（t_i）\} _ i $的极限上限的凸壳。可以进一步简化此特征。实际上，我们证明了不需要凸壳的$ t $的分解。
In this note we characterize the essential numerical range of a block diagonal o\-pe\-ra\-tor $T=\bigoplus_i T_i$ in terms of the numerical ranges $\{W(T_i)\}_i$ of its components. Specifically, the essential numerical range of $T$ is the convex hull of the limit superior of $\{W(T_i)\}_i$. This characterization can be simplified further. In fact, we prove the existence of a decomposition of $T$ for which the convex hull is not required.
