Annals of Functional Analysis

Invariant subspaces of composition operators on a Hilbert space of Dirichlet series

Maofa Wang and Xingxing Yao

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Abstract

In this paper, we study invariant subspaces of composition operators on the Hilbert space of Dirichlet series with square summable coefficients. The structure of invariant subspaces of a composition operator is characterized, and the strongly closed algebras generated by some composition operators with irrational symbols are shown to be reflexive. As an application, we provide a criterion for composition operators with certain symbols not to be algebraic.

Article information

Source
Ann. Funct. Anal., Volume 6, Number 4 (2015), 179-190.

Dates
First available in Project Euclid: 1 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.afa/1435764010

Digital Object Identifier
doi:10.15352/afa/06-4-179

Mathematical Reviews number (MathSciNet)
MR3365990

Zentralblatt MATH identifier
1330.47031

Subjects
Primary: 47B33: Composition operators
Secondary: 30D55 46E15: Banach spaces of continuous, differentiable or analytic functions

Keywords
Dirichlet series composition operator invariant subspace algebraic operator

Citation

Wang, Maofa; Yao, Xingxing. Invariant subspaces of composition operators on a Hilbert space of Dirichlet series. Ann. Funct. Anal. 6 (2015), no. 4, 179--190. doi:10.15352/afa/06-4-179. https://projecteuclid.org/euclid.afa/1435764010


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