On the convergence of sequences of weighted composition operators on certain weighted Hardy spaces

Let H-2(beta) be a weighted Hardy space. In this paper under certain conditions on H-2(beta), convergence of a sequence of weighted composition operators in the weak, strong and uniform operator topologies, in terms of the convergence of the corresponding sequences of inducing maps are investigated. Let C-psi,C-phi be a bounded weighted composition operator and {C-psi,phi(n)} be the sequence of its powers. Under certain conditions on H-2(beta), phi and psi we investigate convergence of the induced weighted composition operators C-psi,phi(n). Let A(G)(2) be a weighted Bergman space. In this paper we investigate convergence of a sequence of weighted composition operators in the Hilbert Schmidt norm in terms of the convergence of the corresponding sequences of inducing maps.