Shift invariant subspaces of composition operators.

Article

Jones, M. 2005. Shift invariant subspaces of composition operators. Archiv der Mathematik. 84 (3), pp. 258-267. https://doi.org/10.1007/s00013-004-1017-z
TypeArticle
TitleShift invariant subspaces of composition operators.
AuthorsJones, M.
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.

JournalArchiv der Mathematik
ISSN1420-8938
Publication dates
Print01 Mar 2005
Publication process dates
Deposited02 Dec 2008
Output statusPublished
Digital Object Identifier (DOI)https://doi.org/10.1007/s00013-004-1017-z
LanguageEnglish
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