广义Kato分解与Weyl型定理的摄动

Generalized Kato Decomposition and Perturbations for the Weyl Type Theorem

称T∈B(H)有广义Kato分解,若存在一对T的闭的不变子空间(M,N)使得H=M⊕Ⅳ,其中T|_M为上半Fredholm算子且具有非负的指标,T|_N是幂零的本文利用算子的广义Kato分解性质,研究了Weyl型定理在紧摄动下的稳定性.此外还研究了2×2上三角算子矩阵的Weyl型定理在紧摄动下的稳定性.

An operator T ∈ B（H） is said to admit a generalized Kato decomposition, if there exists a pair of T-invariant closed subspaces （M｜ N） such that H=M ⊕ N, the restriction T｜M is upper semi-Fredholm with ind（T｜M） ≤ 0 and TIjv is nilpotent. In this paper, using the property of generalized Kato decomposition of T E B（H）, we investigate the stability of the Weyl type theorem under compact perturbations. Also, we characterize 2 × 2 upper triangular operator matrices for which the Weyl type theorem is stable under compact perturbations.