Normaloid weighted composition operators on H2

Abstract

When φ is an analytic self-map of the unit disk with Denjoy–Wolff point a∈D, and ρ(Wψ,φ)=ψ(a), we give an exact characterization for when Wψ,φ is normaloid. We also determine the spectral radius, essential spectral radius, and essential norm for a class of non-power-compact composition operators whose symbols have Denjoy–Wolff point in D. When the Denjoy–Wolff point is on ∂D, we give sufficient conditions for several new classes of normaloid weighted composition operators.