Weighted composition operators on unitarily invariant spaces on the unit ball

Given a reproducing kernel Hilbert space of holomorphic functions on the unit ball of ℂ^𝑛 it is quite natural to ask what the unitaries of this space look like. Of particular interest to us is the question of when a weighted composition operator (WCO) on this given space defines a unitary. In 2020 Martín, Mas and Vukotíc considered WCOs on a large class of reproducing kernel Hilbert spaces of holomorphic functions on the unit disc 𝔻. The authors then showed that in this setting, a WCO is unitary if and only if it is co-isometric, while additionally characterizing when this is the case. In this talk, we will generalize this result to the unit ball. This is joint work with Michael Hartz.