Self-adjoint, unitary, and normal weighted composition operators in several variables

We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form ( 1 − 〈 z , w 〉 ) − γ for γ > 0 . We find necessary and sufficient conditions for the adjoint of a weighted composition operator to be a weighted composition operator or the inverse of a weighted composition operator. We then obtain characterizations of self-adjoint and unitary weighted composition operators. Normality of these operators is also investigated.