关于超递归算子
On super-recurrent operators
摘要：
本文引入并研究了算子超常返的概念。我们研究了这类算子的一些性质，并证明了它与超循环算子和常返算子有一些共同的性质。特别是，我们表明，如果$T$是超递归的，那么$σ(T)$和$σ_p(T^*)$，$T$的谱和$T^*$的点谱，分别有一些值得注意的性质。
英文摘要：
In this paper, we introduce and study the notion of super-recurrence of operators. We investigate some properties of this class of operators and show that it shares some characteristics with supercyclic and recurrent operators. In particular, we show that if $T$ is super-recurrent, then $σ(T)$ and $σ_p(T^*)$, the spectrum of $T$ and the point spectrum of $T^*$ respectively, have some noteworthy properties.
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