Shift invariant subspaces of composition operators.

Jones, Matthew ORCID: https://orcid.org/0000-0002-5252-5234 (2005) Shift invariant subspaces of composition operators. Archiv der Mathematik, 84 (3) . pp. 258-267. ISSN 1420-8938 [Article] (doi:10.1007/s00013-004-1017-z)

Abstract

Let C denote the composition operator defined on the standard Hardy spaces Hp as where is an analytic self-map of the unit disk in the complex plane. In this paper we discuss those invariant subspaces of C in Hp which are invariant under the shift operator, We restrict our attention to the case where is an inner function. Our main result characterises these invariant subspaces. We also consider C when restricted to such an invariant subspace and we describe the structure of the operator and find a formula for the essential spectral radius.

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