%0 Unpublished work %T Some revisited results about composition operators on Hardy spaces %+ Laboratoire de Mathématiques de Lens (LML) %+ Laboratoire Paul Painlevé (LPP) %+ Departamento de Analisis Matematico %A Lefèvre, Pascal %A Li, Daniel %A Queffélec, Hervé %A Rodriguez-Piazza, Luis %Z 21 pages %8 2010-01-19 %D 2010 %Z 1001.3328 %K Blaschke product %K Carleson function %K Carleson measure %K composition operator %K Hardy-Orlicz space %K Nevanlinna counting function %K Schatten classes %Z MSC: Primary: 47B33 -- Secondary: 47B10 %Z Mathematics [math]/Functional Analysis [math.FA]Preprints, Working Papers, ... %X 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. %G English %2 https://univ-artois.hal.science/hal-00448623/document %2 https://univ-artois.hal.science/hal-00448623/file/Comp_revisited.pdf %L hal-00448623 %U https://univ-artois.hal.science/hal-00448623 %~ UNIV-ARTOIS %~ CNRS %~ INSMI %~ UNIV-LILLE %~ LML %~ LPP-MATH