局部单值扩张性:拓扑一致降指数谱与Drazin谱

Topological Uniform Decent Spectrum and Drazin Spectrum Through Localized SVEP

设X是Banach空间,T是X上的有界线性算子,记复平面上使得T在λ没有单值扩张性的点λ全体为S(T).通过S(T)建立了左Drazin谱与拓扑一致降指数谱之间的等式以及左Drazin谱与拟Fredholm谱之间的等式;利用S(T*)建立了降指数谱与拓扑一致降指数谱之间的等式以及右Drazin谱与拟Fredholm谱之间的等式.并给出了这些结果在有拓扑一致降指数的算子的幂零摄动及算子矩阵的拓扑一致降指数谱方面的一些应用.

Let X be a Banach space and T be a bounded linear operator on X. It denotes by S（7＇） the set of all complex h E C such that T does not have the single-valued extension property at A. In this note, it proves equality up to S（T） between the left Drazin spectrum and the topological uniform descent spectrum, the left Drazin spectrum and the quasi-Fredholm spectrum, equality up to S（T＇） between the descent spectrum and the topological uniform descent spectrum, the right Drazin spectrum and the quasi-Fredholm spectrum. It also gives some applications of these results on the nilpotent perturbation of operators with topological uniform descent and the topological uniform spectrum of the operator matrices.