性质(N)的摄动及其直和

Perturbations of Property(N) and its Direct Sum

引入了新的谱性质(N)的概念,从而再次推广了Weyl型定理,并讨论了谱性质(N)与其他Weyl型定理的关系.同时,探讨了它在可交换幂零算子、拟幂零算子、有限秩算子和Riesz算子摄动下的稳定性.最后探究了性质(N)的直和结果.

It introduces a new concept of spectral property （N）, which extends Weyl type theorem again, and discusses relations between property （N） and other Weyl type theorems. At the same time, this paper considers its preservation under perturbations stability by commuting nilpotent, quasi-nilpotent, finite rank and Riesz operators. Finally, this paper explores direct sum of property （N）.