Commutants of complex symmetric weighted composition operators on Fock space

Abstract

In this paper, we investigate weighted composition operators $W_{f,g}$ commuting with complex symmetric weighted composition operators $W_{ψ, φ}$ on the classical Fock space $\mathcal{F}^{2}(\mathbb{C})$. In particular, we investigate the symbols $f$ and $g$ give rise to $W_{f,g}$ commuting with a complex symmetric weighted composition operator on $\mathcal{F}^{2}$. We further characterize when the commuting weighted composition operators are self-adjoint and normal.