Supercyclicity and resolvent condition for weighted composition operators (Q2120946)

Let \(u\) and \(\psi\) be entire functions. This article presents a few results about weighted composition operators \(W_{u,\psi} f := u (f \circ \psi)\) acting on the Fock space \(\mathcal{F}_p, \ 1 \leq p < \infty\). It is proved that no weighted composition operator on Fock spaces is supercyclic. Conditions under which the operators satisfy Ritt's resolvent growth condition are also identified. In particular, it is shown that a non-trivial composition operator \(C_{\psi}\) on a Fock space satisfies such a growth condition if and only if it is compact.