$ε$-hypercyclic operators that are not $δ$-hypercyclic for $δ$ < $ε$

Frédéric Bayart

Published 2023-03-29Version 1

For every fixed $\epsilon$ $\in$ (0, 1), we construct an operator on the separable Hilbert space which is $\delta$-hypercyclic for all $\delta$ $\in$ ($\epsilon$, 1) and which is not $\delta$-hypercyclic for all $\delta$ $\in$ (0, $\epsilon$).