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SHIFT-INVARIANT SUBSPACES INVARIANT FOR COMPOSITION OPERATORS ON THE HARDY-HILBERT SPACE.
- Source :
-
Proceedings of the American Mathematical Society . Dec2014, Vol. 142 Issue 12, p4143-4154. 12p. - Publication Year :
- 2014
-
Abstract
- If φ is an analytic map of the unit disk D into itself, the composition operator Cφ on a Hardy space H² is defined by Cφ(f) = f o φ. The unilateral shift on H² is the operator of multiplication by z. Beurling (1949) characterized the invariant subspaces for the shift. In this paper, we consider the shift-invariant subspaces that are invariant for composition operators. More specifically, necessary and sufficient conditions are provided for an atomic inner function with a single atom to be invariant for a composition operator, and the Blaschke product invariant subspaces for a composition operator are described. We show that if has Denjoy-Wolff point a on the unit circle, the atomic inner function subspaces with a single atom at a are invariant subspaces for the composition operator Cφ. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 142
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 98854635
- Full Text :
- https://doi.org/10.1090/S0002-9939-2014-12132-0