Compact linear combinations of composition operators induced by linear fractional maps

摘要

It has been known that the difference of two composition operators induced by linear fractional self-maps of a ball cannot be nontrivially compact on either the Hardy space or any standard weighted Bergman space. In this paper we extend this result in two significant directions: the difference is extended to general linear combinations and inducing maps are extended to linear fractional maps taking a ball into another possibly of different dimension.