关于强不可约算子小紧摄动的一个注记

A Note on the Small Compact Perturbations of Strongly Irreducible Operators

在有有限维Schauder分解空间上讨论强不可约算子的小紧摄动问题,证明了有有限维Schauder分解空间上的具有单点谱的对角算子均可小紧摄动成为强不可约算子.

Discusses the problem of small compact perturbations of strongly irreducible operators on Banach spaces with finite dimensional Schauder decompositions.It shows that every diagonal operator with a connected spectrum on such class of Banach spaces is a small compact perturbation of a strongly irreducible operator.