Weighted composition operators that preserve p-frames

Abstract

We establish the equivalence between being invertible and preserving p-frames for weighted composition operators on the unit disk. Moreover, we obtain the symbol properties of the bounded invertible operators. Based on those results, we prove that for the weighted Bergman spaces Aap(dAα), Besov spaces Bp and weighted Dirichlet spaces Dα2, weighted composition operators preserve p-frames on X if and only if they preserve q-Riesz bases on X⁎, and obtain related application on dynamical sampling of weighted composition operators. Furthermore, we characterize the equivalence between Fredholmness and the invertibility of weighted composition operators.