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arXiv · 1001.3328

Some revisited results about composition operators on Hardy spaces

Pascal Lefèvre·Daniel Li·Hervé Queffélec·Luis Rodriguez-Piazza
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Abstract

We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces $H^Ψ$: construction of a "slow" Blaschke product giving a non-compact composition operator on $H^Ψ$; construction of a surjective symbol whose composition operator is compact on $H^Ψ$ and, moreover, is in all the Schatten classes $S_p (H^2)$, $p > 0$. On the other hand, we revisit the classical case of composition operators on $H^2$, giving first a new, and simplier, characterization of closed range composition operators, and then showing directly the equivalence of the two characterizations of membership in the Schatten classes of Luecking and Luecking and Zhu.

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Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza. 2010-01-19. Some revisited results about composition operators on Hardy spaces. https://arxiv.org/abs/1001.3328

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