International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 4, Pages 239-248
doi:10.1155/S0161171201003726

Geometric properties of composition operators belonging to Schatten classes

Abstract

We investigate the connection between the geometry of the image domain of an analytic function mapping the unit disk into itself and the membership of the composition operator induced by this function in the Schatten classes. The purpose is to provide solutions to Lotto's conjectures and show a new compact composition operator which is not in any of the Schatten classes.