Integral Equations and Operator Theory

, Volume 40, Issue 4, pp 481–494

Topological structure of the space of composition operators onH

  • Barbara Maccler
  • Shûichi Ohno
  • Ruhan Zhao
Article

DOI: 10.1007/BF01198142

Cite this article as:
Maccler, B., Ohno, S. & Zhao, R. Integr equ oper theory (2001) 40: 481. doi:10.1007/BF01198142
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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 

Copyright information

© Birkhäuser Verlag 2001

Authors and Affiliations

  • Barbara Maccler
    • 1
  • Shûichi Ohno
    • 2
  • Ruhan Zhao
    • 1
  1. 1.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA
  2. 2.Department of MathematicsNippon Institute of TechnologyMinami-SaitamaJapan

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