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Some revisited results about composition operators on Hardy spaces

 

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Author: Lefèvre, Pascal
Li, Daniel
Queffélec, Hervé
Rodríguez Piazza, Luis
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2012
Published in: Revista Matemática Iberoamericana, 28 (1), 57-76.
Document type: Article
Abstract: We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces HΨ: construction of a “slow” Blaschke product giving a non-compact composition operator on HΨ; construction of a surjective symbol whose composition operator is compact on HΨ and, moreover, is in all the Schatten classes Sp(H2), p > 0. On the other hand, we revisit the classical case of composition operators on H2, 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.
Cite: Lefèvre, P., Li, D., Queffélec, H. y Rodríguez Piazza, L. (2012). Some revisited results about composition operators on Hardy spaces. Revista Matemática Iberoamericana, 28 (1), 57-76.
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URI: http://hdl.handle.net/11441/46376

DOI: 10.4171/RMI/666

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