ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 47B38 Ohno, Shûichi, Nippon Institute of Technology, Japan: Zhao, Ruhan, Kyoto University, Japan Topological structure of the space of composition operators on H^{∞} Components and isolated points of the topological space of composition operators on H^{∞} in the uniform operator topology are characterized. Compact differences of two composition operators are also characterized. With the aid of these results, we show that a component in C(H^{∞}) is not the set of all composition operators that differ from the given one by a compact operator.