关于幂有限秩算子

On Power Finite Rank Operators

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

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.