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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Representations of compact groups on topological vector spaces: some remarks


Author: Russell A. Johnson
Journal: Proc. Amer. Math. Soc. 61 (1976), 131-136
MSC: Primary 22C05; Secondary 22D12
MathSciNet review: 0430144
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Abstract: A standard theorem concerning the decomposition of a representation of a compact group on a Hilbert space $ E$ is generalized to the case when $ E$ is locally convex and quasi-complete. As a corollary, it is shown that if $ E$ is topologically irreducible, then it is finite dimensional.


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  • [2] Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496 (81k:43001)
  • [3] Garth Warner, Harmonic analysis on semi-simple Lie groups. I, Springer-Verlag, New York-Heidelberg, 1972. Die Grundlehren der mathematischen Wissenschaften, Band 188. MR 0498999 (58 #16979)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0430144-6
PII: S 0002-9939(1976)0430144-6
Article copyright: © Copyright 1976 American Mathematical Society