性质$(\omega )$是Weyl定理的一种变形.文章中将算子的一致Fredholm指标性质用于性质$(\omega )$的判定中.根据一致Fredholm指标性质定义出一种新的谱集,
通过该谱集和算子的拓扑一致降标之间的关系,给出了有界线性算子与其共轭算子同时满足性质$(\omega )$的充要条件.之后, 研究了算子矩阵的$(\omega )$性质.

Property $(\omega )$ is a variant of Weyl's theorem. By the property of consistence in Fredholm index, the judgement of property  $(\omega )$ is studied. Using the relation between a new spectrum defined in  view of the property of consistence in Fredholm index and the topological   uniform descent,
   the necessary and sufficient condition for an operator and its  conjugate to satisfy property $(\omega )$ are given. In addition,  the property $(\omega )$
of operator matrices is studied.