关于算子谱性质幂有限秩摄动的一个注记

A note on power finite rank perturbations of spectral properties

针对性质(v)和性质(gv)的摄动稳定性问题,通过研究性质(aw)与性质(gaw)的可交换幂有限秩摄动稳定性的相关结果,同时结合性质(aw)与性质(v)、性质(gaw)与性质(gv)之间的关系,为证明性质(v)和性质(gv)在可交换幂有限秩摄动下保持稳定提供了新的方法.

To study the perturbation results of properties(v)and(gv),we provide a new approach to the commuting finite rank perturbations of properties(v)and(gv)by combining the relation of them to properties(aw)and(gaw)and utilizing the perturbation results of properties(aw)and(gaw).