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## Some revisited results about composition operators on Hardy spaces

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Pascal Lefèvre
Daniel Li
Hervé Queffélec
• Function : Author
• PersonId : 859618
Luis Rodriguez-Piazza
• Function : Author
• PersonId : 859619

#### 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.

#### Domains

Mathematics [math] Functional Analysis [math.FA]

### Dates and versions

hal-00448623 , version 1 (19-01-2010)

### Identifiers

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

### Cite

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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