The Exact $\epsilon$-Hypercyclicity Threshold

Abstract

In this paper we give an affirmative answer to the problem proposed by Bayart in [J. Math. Anal. Appl. \textbf{529} (2024), 127278]: given $\epsilon \in (0,1)$, there exists an operator which is $\hat{I}´$-hypercyclic if and only if $\hat{I}´\in [\epsilon ,1)$?

12 pages