Self-adjoint, unitary, and normal weighted composition operators in several variables
arXiv:1207.5980 · doi:10.1016/j.jmaa.2012.05.065
Abstract
We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form for . 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.