Abstract
The aim of this paper is to answer the following question concerning invariant subspaces of composition operators: characterize φ, holomorphic self maps of D, and inner functions θ∈H∞(D) such that the Beurling type invariant subspace θH2 is an invariant subspace for Cφ. We prove the following result: Cφ(θH2)⊆θH2 if and only if θ∘φθ∈S(D). This classification also allows us to recover or improve some known results on Beurling type invariant subspaces of composition operators.
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