International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 4, Pages 239-248

Geometric properties of composition operators belonging to Schatten classes

Yongsheng Zhu

Fair Isaac 2150 Shattuck Avenue, Berkeley, CA 94704, USA

Received 9 August 1999

Copyright © 2001 Yongsheng Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.