Invertible weighted composition operators

A weighted composition operator Cψ,ϕ takes an analytic map f on the open unit disc of the complex plane to the analytic map ψ · f ◦ ϕ where ϕ is an analytic map of the open unit disc into itself and ψ is an analytic map on the open unit disc. This paper studies the invertibility of such operators. The two maps ψ and ϕ are characterized when Cψ,ϕ acts on the Hardy–Hilbert space of the unit disc H2(D). Depending upon the nature of the fixed points of ϕ spectra are then investigated. © 2011 Elsevier Inc. All rights reserved.