Which linear-fractional composition operators are essentially normal?☆

By Paul S. Bourdon, D. Levi, S. Narayan, J. H. Shapiro. 2003

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Toeplitz-Composition C*-Algebras (2006, background): “In the course of their work on essentially normal linear-fractional composition operators, Bourdon, Levi, Narayan and Shapiro [3] show that if ϕ is a linear fractional non-automorphism mapping D into D and fixing a point of ∂D, then [T ∗z , Cϕ] is compact, where Tz is the shift on H 2.”