$\epsilon$-hypercyclic operators that are not $\delta$-hypercyclic for $\delta$ < $\epsilon$

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, $\epsilon$).

Keywords

Mathematics - Functional Analysis

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