Ching-on Lo
We characterize all weighted composition operators v C ψ vC_{\psi } that commute with a J μ J_{\mu } -symmetric weighted composition operator u C φ uC_{\varphi } on the reproducing kernel Hilbert space H γ H_{\gamma } of analytic functions on the unit disk D {\mathbb D} . It turns out these commuting operators v C ψ vC_{\psi } are necessarily J μ J_{\mu } -symmetric. Furthermore, we obtain characterization(s) for the commuting operator v C ψ vC_{\psi } to be self-adjoint, normal or unitary.