A new proof of a Nordgren, Rosenthal and Wintrobe Theorem on universal operators

Source abstract

A striking result by Nordgren, Rosenthal and Wintrobe states that the Invariant Subspace Problem is equivalent to the fact that any minimal invariant subspace for a composition operator C φ C_{\varphi } induced by a hyperbolic automorphism φ \varphi of the unit disc D \mathbb {D} acting on the classical Hardy space H 2 H^2 is one dimensional. We provide a completely different proof of Nordgren, Rosenthal and Wintrobe’s Theorem based on analytic Toeplitz operators.