#### Vol. 14, No. 2, 2021

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Two families of hypercyclic nonconvolution operators

### Alexander Myers, Muhammadyusuf Odinaev and David Walmsley

Vol. 14 (2021), No. 2, 349–360
##### Abstract

Let $H\left(ℂ\right)$ be the set of all entire functions endowed with the topology of uniform convergence on compact sets. Let $\lambda ,b\in ℂ$, let ${C}_{\lambda ,b}:H\left(ℂ\right)\to H\left(ℂ\right)$ be the composition operator ${C}_{\lambda ,b}f\left(z\right)=f\left(\lambda z+b\right)$, and let $D$ be the derivative operator. We extend results on the hypercyclicity of the nonconvolution operators ${T}_{\lambda ,b}={C}_{\lambda ,b}\circ D$ by showing that whenever $|\lambda |\ge 1$, the collection of operators

forms an algebra under the usual addition and multiplication of operators which consists entirely of hypercyclic operators (i.e., each operator has a dense orbit). We also show that the collection of operators

consists entirely of hypercyclic operators.

##### Keywords
hypercyclic operators, nonconvolution operators
Primary: 47A16