A NOTE ON FREQUENT HYPERCYCLICITY OF OPERATORS THAT $$\lambda$$-COMMUTE WITH THE DIFFERENTIATION OPERATOR

Abstract A continuous linear operator on a Fréchet space $$\mathcal {X}$$ X is frequently hypercyclic if there exists vector x such that for any nonempty open subset $$U\subset \mathcal U ⊂ the set of $$n\in \mathbb {N}\cup \{0\}$$ n ∈ N ∪ { 0 } which $$T^nx\in U$$ T x has positive lower density. Here we determine when an commutes up to factor with differentiation D , defined entire functions, hypercyclic.