On super-recurrent operators

TL;DR

This paper introduces the concept of super-recurrence in operators, exploring its properties and spectral characteristics, and comparing it with supercyclic and recurrent operators.

Contribution

It defines super-recurrence for operators and analyzes its spectral properties, highlighting similarities with existing classes like supercyclic and recurrent operators.

Findings

Super-recurrent operators have distinctive spectral properties.

Super-recurrence shares characteristics with supercyclic and recurrent operators.

Spectral analysis reveals noteworthy features of 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 $\sigma_p(T^*)$, the spectrum of $T$ and the point spectrum of $T^*$ respectively, have some noteworthy properties.