关于线性算子谱的非半Fredholm域

On The Non-semi-Fredholm Domain of the Spectra of Linear Operator

本文研究Hilbert空间上有界线性算子谱的非半Fredholm域各部分的拓扑结构及其在紧摄动下的变化,证明了,其中是开集,是至多可列集,且的每个连通分支都能经T的一次紧摄动而全部“正则化”。本文的结果推广并加强了[2],[3],[4]的有关结论。

In this article, we investigate the topological structure and the variation under compact perturbation of the parts of non-semi-Fredholm domain of the spectrum for a bounded linear operator on Hilbert space. We show that ψ_(∞e)(T)=∪ ψ_(∞∞)(T +K) =(ψ_(∞e)(T))^(er)∪(ψ(∞e)(T))^(es), where (ψ_(∞e)(T))^(er) is an open set and (ψ_(∞e)(T))^(es) is a denumerable set, we show that every connected component of (ψ_(∞e)(T))^(er) can be 'regularized' as a whole by a eompact perturbation of T. Our results generalize and strengthen the related conclusions in [2],[3],[4].