Abstract
We give necessary and sufficient conditions for a composition operator with Dirichlet series symbol to belong to the Schatten classes S_{p} of the Hardy space \mathcal{H}^{2} of Dirichlet series. For p\geq 2 , these conditions lead to a characterization for the subclass of symbols with bounded imaginary parts. Finally, we establish a comparison-type principle for composition operators. Applying our techniques in conjunction with classical geometric function theory methods, we prove the analogue of the polygonal compactness theorem for \mathcal{H}^{2} and we give examples of bounded composition operators with Dirichlet series symbols on \mathcal{H}^{p} , p>0 .
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