Weighted composition operators on Fock spaces and their dynamics

TL;DR

This paper characterizes bounded and compact weighted composition operators on Fock spaces and proves they cannot be supercyclic, providing insights into their structure and dynamic properties.

Contribution

It offers a detailed characterization of bounded and compact weighted composition operators on Fock spaces and establishes their non-supercyclic nature.

Findings

Characterization of bounded weighted composition operators

Characterization of compact weighted composition operators

Weighted composition operators are not supercyclic

Abstract

Bounded weighted composition operators, as well as compact weighted composition operators, on Fock spaces have been characterised. This characterisation is refined to the extent that the question of whether weighted composition operators on the Fock space can be supercyclic is answered in the negative.