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

For every fixed epsilon is an element of (0, 1), we construct an operator on the separable Hilbert space which is 5-hypercyclic for all delta is an element of (epsilon, 1) and which is not 5-hypercyclic for all delta is an element of (0, epsilon).(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

The passage describes the construction of an operator on a separable Hilbert space that is 5-hypercyclic for all δ in the range (ε, 1) and is not 5-hypercyclic for all δ in the range (0, ε).