Invertible weighted composition operators

Abstract

A weighted composition operator C ψ , 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 C ψ , φ acts on the Hardy–Hilbert space of the unit disc H 2 ( D ) . Depending upon the nature of the fixed points of φ spectra are then investigated.