Essential spectra of composition operators on Hardy spaces
by
Ugur Gül
Sabanci University

In this work we study the essential spectrum of composition operators on the Hardy space of the unit disc and of the upper half plane. We completely characterize the essential spectrum of the class of composition operators acting on H^p for 1 < p < ∞ that are induced by analytic self-maps b of the upper half-plane which satisfy the conditions:

i) p(z) = b(z) - z is a bounded analytic function on the upper half-plane H which is analytic across R and analytic at infinity,

ii) the closure of the image of H under p is compact in H.

Date received: April 6, 2008