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Some revisited results about composition operators on Hardy spaces

2010/01/19 by Pascal Lefèvre, Lefèvre, Pascal, Li, Daniel +4
Mathematics · #47B10 (Secondary) #47B33 (Primary) #Advanced Banach Space Theory #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · doi:10.48550/arxiv.1001.3328

openalex publication_date 2010/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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