S.G理论在研究Semi—Fredholm算子时的应用

Applications of S. G Theory in Studying Semi-Fredholm Operators

本文研究了具有有限升标(降标)的半Fredholm算子,证明了具有有限升标(降标)的上半Fredholm算子在其摄动类中交换元的摄动下仍具有同样性质,对于下半Fredholm算子有同样结论.从而改进了[1,2]中的主要结果.同时,我们证明了被摄动算子集合扩大(相对于[1]而言)而摄动仍为紧摄动时较[1]中更强的结果.

In this paper, we prove that the collection of upper semi-Fredholm operators with finite ascent (descent) is closed under commuting operator perturbation class associated with it, and the same thing hold for lower semi-Fredholm operators. As a corrollary, we get the results of [1,2]. At the same time, we also discussed the case when the set being perturbateed are extended, while the compact perturbation is kept.