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 $W_{\psi ,\phi }$ 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.

arXiv comment10 pages paper