Some new properties of composition operators associated with lens maps

Pascal Lefèvre (1) , Daniel Li (1) , Hervé Queffélec (2) , Luis Rodriguez-Piazza (3)

1 LML - Laboratoire de Mathématiques de Lens
2 LPP - Laboratoire Paul Painlevé
3 Departamento de Analisis Matematico

We give examples of results on composition operators connected with lens maps. The first two concern the approximation numbers of those operators acting on the usual Hardy space $H^2$. The last ones are connected with Hardy-Orlicz and Bergman-Orlicz spaces $H^\psi$ and $B^\psi$, and provide a negative answer to the question of knowing if all composition operators which are weakly compact on a non-reflexive space are norm-compact.

Keywords: approximation numbers; Carleson measure; compact operator; composition operator; Dunford-Pettis operator; Hardy space; lens map; Orlicz function; Orlicz space; Schatten classes; weakly compact operator

Domains: Mathematics [math]; Functional Analysis [math.FA]

Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza. Some new properties of composition operators associated with lens maps. 2012. ⟨hal-00656038⟩