Complex symmetric difference of weighted composition operators on Fock space

Abstract

The aim of the present paper is to completely characterize complex symmetric difference of weighted composition operators $W_{e^{\overline{p}z,az+b}}$ with the conjugations $J$ and $J_{r,s,t}$ defined by $Jf(z)=\overline{f(\bar{z})}$ and $J_{r,s,t}f(z)=te^{sz}\overline{f(\overline{rz+s})}$
on Fock space by building the relations between the parameters $a$, $b$, $p$, $r$ and $s$. As an application, an interesting phenomenon that each operator $W_{e^{\overline{p}z,az+b}}$ is not complex symmetric on Fock space with $J_{s,t,r}$ but their difference is complex symmetric on Fock space has been discovered.