The quadratic numerical range has an important application to the spectral distribution of operators. In this paper, the geometry of the quadratic numerical range is investigated. Moreover, some sufficient conditions for the quadratic numerical range to consist of two disjoint components are discussed. Finally, the necessary and sufficient condition for the quadratic numerical range to be contained in a straight line is given.

中文翻译：

---

关于 2 × 2 块算子矩阵的二次数值范围的几何

二次数值范围对算子的谱分布有重要的应用。在本文中，研究了二次数值范围的几何。此外，讨论了二次数值范围由两个不相交的分量组成的一些充分条件。最后给出了二次数值范围包含在一条直线上的充要条件。