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Archiv der Mathematik

, Volume 84, Issue 3, pp 258–267 | Cite as

Shift invariant subspaces of composition operators on H p

  • M. M. JonesEmail author
Original Paper

Abstract.

Let Cφ denote the composition operator defined on the standard Hardy spaces H p as \(f \mapsto f \circ \varphi ,\) where φ is an analytic self-map of the unit disk in the complex plane. In this paper we discuss those invariant subspaces of Cφ in H p which are invariant under the shift operator, \(\mathfrak{G}f(z) = zf(z).\) We restrict our attention to the case where φ is an inner function. Our main result characterises these invariant subspaces. We also consider Cφ when restricted to such an invariant subspace and we describe the structure of the operator and find a formula for the essential spectral radius.

Mathematics Subject Classification (2000).

47B33 47A15 32A35 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Middlesex UniversityLondonUnited Kingdom

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