Integral Equations and Operator Theory

, Volume 12, Issue 5, pp 725–738

Components in the space of composition operators

  • Barbara D. MacCluer

DOI: 10.1007/BF01194560

Cite this article as:
MacCluer, B.D. Integr equ oper theory (1989) 12: 725. doi:10.1007/BF01194560


We consider the topological space of all composition operators, acting on certain Hilbert spaces of holomorphic functions on the unit disc, in the uniform operator topology. A sufficient condition is given for the component of a composition operator to be a singleton. A necessary condition is given for one composition operator to lie in the component of another. In addition, we prove analogous results for the component of the image of a composition operator in the Calkin algebra. Finally, we obtain some related results on the essential norm of a linear combination of composition operators.

Copyright information

© Birkhäuser Verlag 1989

Authors and Affiliations

  • Barbara D. MacCluer
    • 1
  1. 1.Department of MathematicsUniversity of RichmondRichmond