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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.
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, January 21, 2022 - 3:30:41 AM
Long-term archiving on: : Thursday, June 17, 2010 - 9:35:48 PM
Contributor : Daniel Li Connect in order to contact the contributor
Submitted on : Tuesday, January 19, 2010 - 3:19:35 PM
Last modification on : Friday, January 21, 2022 - 3:30:41 AM
Long-term archiving on: : Thursday, June 17, 2010 - 9:35:48 PM
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