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

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.