Compact differences of weighted composition operators on \(H^\infty(B_N)\) (Q2912669)

Let \(B_N\) be the unit ball of \(\mathbb C^N\). A weighted composition operator is an operator of the form \(f\mapsto u(f\circ \phi)\) for \(f\) analytic on \(B_N\), where \(u\) is an analytic function on \(B_N\) and \(\phi\) is an analytic self map of \(B_N\).NEWLINENEWLINEIn this paper, the author obtains a characterization for the difference of two weighted composition operators to be compact on the space \(H^\infty(B_N)\). The characterization involves certain cancellation conditions for the inducing functions near the boundary and is too technical to be stated here. The author also obtains a sufficient condition for two weighted composition operators to lie in the same component of the space of all nonzero weighted composition operators.