On super-recurrent operators

Abstract

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 $\sigma (T)$ and ${\sigma }_p(T^{\ast })$, the spectrum of $T$ and the point spectrum of $T^{\ast }$ respectively, have some noteworthy properties.

9 pages