Article

Integral Equations and Operator Theory

, Volume 40, Issue 4, pp 481-494

Topological structure of the space of composition operators onH

  • Barbara MacclerAffiliated withDepartment of Mathematics, University of Virginia
  • , Shûichi OhnoAffiliated withDepartment of Mathematics, Nippon Institute of Technology
  • , Ruhan ZhaoAffiliated withDepartment of Mathematics, University of Virginia

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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.

1991 Mathematical subject classification

47B38