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manuscripta mathematica

, Volume 22, Issue 3, pp 293–310 | Cite as

Representations approchees d'un groupe dans une algebre de banach

  • Pierre de la Harpe
  • Max Karoubi
Article

Abstract

Let T be a continuous map from a compact group G to the group of invertible bounded linear operators on a Hilbert space H, the latter being endowed with the norm topology. If the norms ‖T(gh)-T(g)T(h)‖ are small enough (g,h ∈ G), we show that T is a small perturbation of some norm continuous representation of G on H.

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References

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    De La HARPE P. et KAROUBI M.: “Perturbations compactes des représentations d'un groupe dans un espace de Hilbert, I”. Bull. Soc. math. France, Mémoire 46, 1976, 41–65Google Scholar
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    KALLMAN R.R.: A characterization of uniformly continuous representations of connected locally compact groups. Michigan Math. J. 16 (1969) 257–263.Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Pierre de la Harpe
    • 1
  • Max Karoubi
    • 2
  1. 1.Section de MathématiquesUniversité de GenèveGeneve 24
  2. 2.U.E.R. de MathématiquesUniversité de Paris VIIParis

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