On super-recurrent operators

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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