研究了Weyl定理的一种变化: $(\omega )$性质,利用本质逼近点谱的变形${\sigma }_1(\cdot )$和一致Fredholm指标性质构造的新谱集${\sigma }_2(\cdot )$给出了Hilbert 空间上有界线性算子满足$(\omega )$性质的充要条件, 另外, 还研究了$H(P)$类算子的$(\omega )$性质.

In this paper we study the property (ω), a variant of Weyl’s theorem,and for a bounded linear operator defined on a Hilbert space establish the sufficient
and necessary conditions for which property (ω) holds by use of the variant of the essential approximate point spectrum σ1(·) and the new spectrum σ2(·) defined in view of the property of consistency in Fredholm index. In addition, the property (ω) for H(P) operators is discussed.