A note on frequent hypercyclicity of operators that λ -commute with the differentiation operator

Abstract

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