Invertible Composition Operators:The Product of a Composition Operator with the Adjoint of a Composition Operator

摘要

In this paper, we study the product of a composition operator C_φ with the adjoint of a composition operator C_ψ~? on the Hardy space H~2(D). The order of the product gives rise to two different cases. We completely characterize when the operator C_φC_ψ~? is invertible, isometric, and unitary and when the operator C_ψ~?C_φ is isometric and unitary. If one of the inducing maps ? or ψ is univalent, we completely characterize when C_ψ~?C_φ is invertible.