Hypercyclicity of operators that lambda-commute with the differentiation operator on the space of entire functions

摘要

An operator T acting on a separable F-space X is called hypercyclic if there exists f is an element of X such that the orbit {Tnf} is dense in X. Here we determine when an operator that lambda commutes with the operator of differentiation on the space of entire functions is hypercyclic, extending results by G. Godefroy and J. H. Shapiro [16] and R. M. Aron and D. Markose [1].(c) 2022 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).