| On Power Finite Rank Operators |
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| Key Words:
power finite rank operator Drazin invertible eventual topological uniform descent Riesz operator
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| Fund Project:Supported by the Talents Cultivation Program for Outstanding Youth Scientists in Fujian Universities (Grant Nos.Min Education [2015] 54 and [2016] 23), the National Natural Science Foundation of China (Grant No.11401097) and the Natural Science Foundation of Fujian Province (Grant No.2016J05001). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2019.04.005 |
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