Sequences of Weighted Composition Operators on the Hardy-Hilbert Space

摘要

Let. be an analytic self map of the open unit disc D. Assume that. is an analytic map of D. Suppose that psi is in the Hardy-Hilbert space of the open unit disc H-2. The operator that takes f into psi . f omicron phi is a weighted composition operator, and is denoted by C-Psi,C-phi. In this paper we relate the convergence of the sequence {C-psi n,(phi n)} in different operator topologies to the convergence of the two sequences of maps {phi(n)} and {psi(n)}.