|
| 摘要: |
| 本文研究了无限维Banach空间上满足算子等式组的有界线性算子A和BCk的谱性质,其中k为某个非负整数. 具体而言,设A,B,C是定义在无限维Banach空间X上的有界线性算子满足CkBCk=ACk和CkBAk=Ak+1.本文从正则集的角度证明了算子A和BCk的19类谱是一致的. 特别地,我们利用A和BCk的Fredholm谱相等,获得了A和BCk的广义Drazin-Riesz可逆性是等价的. 这些结果是对Yan[7]中结论的推广. |
| 关键词: 算子等式 正则集 广义Drazin-Riesz逆 |
| DOI： |
| 分类号:O177.2 |
| 基金项目:福建省自然科学基金资助(2022J01104). |
|
| THE COMMON PROPERTIES OF SPECTRA UNDER THE NEW OPERATOR EQUATIONS |
|
KONG Yao-bing,YAN Kai
|
| Abstract: |
| The spectral properties of bounded linear operators A and BCk on inflnitedimensional Banach spaces that satisfy a system of operator equations are studied in this article, where k is some non-negative integer. Speciflcally, let A,B,C be bounded linear operators deflned on the inflnite-dimensional Banach space X satisfying CkBCk=ACk and CkBAk=Ak+1. This paper proves that the 19 types of spectra of operators A and BCk are consistent from the perspective of the regular set. In particular, we use the fact that the Fredholm spectra of A and BCk are equal to obtain that the generalized Drazin-Riesz invertibility of A and BCk is equivalent. These results are a generalization of the conclusions in Yan [7]. |
| Key words: operator equation regularity generalized Drazin-Riesz inverse |
