# Some revisited results about composition operators on Hardy spaces

Abstract : We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces $H^\Psi$: construction of a slow'' Blaschke product giving a non-compact composition operator on $H^\Psi$; construction of a surjective symbol whose composition operator is compact on $H^\Psi$ 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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https://hal-univ-artois.archives-ouvertes.fr/hal-00448623
Contributor : Daniel Li Connect in order to contact the contributor
Submitted on : Tuesday, January 19, 2010 - 3:19:35 PM
Last modification on : Friday, May 6, 2022 - 4:24:08 PM
Long-term archiving on: : Thursday, June 17, 2010 - 9:35:48 PM

### Files

Comp_revisited.pdf
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### Identifiers

• HAL Id : hal-00448623, version 1
• ARXIV : 1001.3328

### Citation

Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza. Some revisited results about composition operators on Hardy spaces. 2010. ⟨hal-00448623⟩

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