A class of C-normal weighted composition operators on quaternionic Fock space

Abstract

Let $W_{\psi ,\phi }$ be the bounded weighted composition operator on quaternionic Fock space $F^2\left(H\right)$ with $\phi \left(p\right)=pa+b$ and slice regular function ψ on $H$. We mainly explore the prerequisites for $C$-normal and $C$-symmetric $W_{\psi ,\phi }$ under $\left|a\right|\le 1$. We further describe the $C_{r,s,t}$-normal $W_{\psi ,\phi }$ and exhibit two examples for binormal weighted composition operator, extending the results on complex Fock space.