Linear Fractional Maps That Induce Compact Linear Operators

Abstract

It is generally known that the difference of two composition operators formed by linear fractional self-maps of a ball cannot be nontrivially compactly contained in the Hardy space or any common weighted Bergman space. This study extends this finding in two important ways: Inducing maps are expanded to linear fractional maps that carry a ball into a second, and the difference is extended to generic linear combinations, potentially higher-dimensional space.