Cyclic and supercyclic weighted composition operators on the Fock space

TL;DR

This paper characterizes when weighted composition operators on the Fock space are cyclic, shows they are not supercyclic, and concludes the space does not support cyclic multiplication operators.

Contribution

Provides a complete characterization of cyclicity for weighted composition operators on the Fock space based on symbol derivatives and zeros, and proves the non-existence of supercyclic and cyclic multiplication operators.

Findings

Cyclic weighted composition operators are characterized by the derivative of the symbol and zeros of the weight.

The Fock space does not support supercyclic weighted composition operators.

The space supports no cyclic multiplication operators.

Abstract

We study the cyclic and supercyclic dynamical properties of weighted composition operators on the Fock space $\mathcal{F}_2$. A complete characterization of cyclicity which depends on the derivative of the symbol for the composition operator and zeros of the weight function is provided. It is further shown that the space fails to support supercyclic weighted composition operators. As a consequence, we also noticed that the space supports no cyclic multiplication operator.