Normaloid Weighted Composition Operators on $H^2$

Abstract: When \ph\ is an analytic self-map of the unit disk with Denjoy-Wolff point $a \in \D$, and $\rho(\W) = \psi(a)$, we give an exact characterization for when \W\ is normaloid. We also determine the spectral radius, essential spectral radius, and essential norm for a class of non-compact composition operators whose symbols have Denjoy-Wolff point in \D. When the Denjoy-Wolff point is on $\partial \D$, we give sufficient conditions for several new classes of normaloid weighted composition operators.