, Volume 40, Issue 4, pp 481-494

Topological structure of the space of composition operators onH

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Abstract

Components and isolated points of the topological space of composition operators onH 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 inC(H ) is not in general the set of all composition operators that differ from the given one by a compact operator.

Supported by the Grant-in-Aid for Scientific Research (C), the Ministory of Education, Science and Culture, No. 09640218, and the Nippon Institute of Technology No. 111
Supported by the Japan Society for the Promotion of Science