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Proceedings of the American Mathematical Society

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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
  • [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

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Article copyright: © Copyright 1976 American Mathematical Society