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| 有一致降指数的算子 | |
| 引用本文： | 陈剑岚,江樵芬,钟怀杰. 有一致降指数的算子[J]. 数学学报, 2010, 53(4): 625-634 |
| 作者姓名： | 陈剑岚 江樵芬 钟怀杰 |
| 作者单位： | 福建师范大学数学与计算机科学学院 福州 350007 |
| 基金项目： | 国家自然科学基金资助项目(10771034);福建省教育厅基金资助项目(JB07047) |
| 摘 要： | 本文讨论了有拓扑一致降指数的算子的可交换拟幂零摄动:举出反例说明有拓扑一致降指数的算子在可交换拟幂零摄动下是不稳定的;得到有拓扑一致降指数的算子和它的可交换拟幂零摄动的超值域与超核之间的关系;利用这些关系,证明了左(右)Drazin可逆算子在可交换幂零摄动下是稳定的.最后还讨论了Banach空间上B-正则类BR_i(1≤i≤13)中算子的R_i型Kato分解与R_i型超Kato分解. |
| 关 键 词： | 一致降指数 拟幂零摄动 超Kato分解 |
| 收稿时间： | 2009-09-02 |
| 修稿时间： | 2009-12-01 |
On Operators with Uniform Descent |
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| Affiliation: | School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, P. R. China |
| Abstract: | We discuss the communicative quasinilpotent perturbation of operators with topological uniform descent: we obtain a counterexample to show that this kind of perturbation isn't stable; and we get the relations between super-ranges and super-kernels of operators with topological uniform descent and their perturbation; by means of these relations, we show that the communicative nilpotent perturbation of left (right) Drazin invertible operators is stable. At last, we also discuss the Ri-type Kato decomposition and Ri-type super-Kato decomposition of operators in the B-regularities BRi(1≤i≤13) on Banach spaces. |
| Keywords: | uniform descent quasinilpotent perturbation super-Kato decomposition |
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