| 曾清平,吴珍莺.关于幂有限秩算子[J].数学研究及应用,2019,39(4):378~382 |
| 关于幂有限秩算子 |
| On Power Finite Rank Operators |
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| DOI：10.3770/j.issn:2095-2651.2019.04.005 |
| 中文关键词: 幂有限秩算子 Drazin可逆 有拓扑一致降指数 黎斯算子 |
| 英文关键词:power finite rank operator Drazin invertible eventual topological uniform descent Riesz operator |
| 基金项目:福建省高校杰出青年科研人才培育计划(Grant Nos.闽教科[2015]54号,闽教科[2016]23号),国家自然科学基金(Grant No.11401097),福建省自然科学基金资助(Grant No.2016J05001). |
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| 中文摘要: |
| 称$F \in \mathcal{B}(X)$是幂有限秩算子,如果存在某个$n \in \mathbb{N}$使得$F^{n}$是有限秩的.本文将给出幂有限秩算子的若干个有趣刻画.特别地,我们证明了幂有限秩算子类恰好是黎斯算子类和有拓扑一致降指数算子类的交集. |
| 英文摘要: |
| An operator $F \in \mathcal{B}(X)$ is called power finite rank if $F^{n}$ is of finite rank for some $n \in \mathbb{N}$. In this note, we provide several interesting characterizations of power finite rank operators. In particular, we show that the class of power finite rank operators is the intersection of the class of Riesz operators and the class of operators with eventual topological uniform descent. |
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