Some new properties of composition operators associated with lens maps

Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza

Published 2012-01-03Version 1

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.