Representations of compact groups on topological vector spaces: some remarks
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- by Russell A. Johnson PDF
- Proc. Amer. Math. Soc. 61 (1976), 131-136 Request permission
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.References
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N. Bourbaki, Éléments de mathématique. Fasc. XIII. Livre VI: Integration, Chaps. 1-4, 2nd ed., Actualités Sci. Indust., no. 1175, Hermann, Paris, 1965. MR 36 #2763.
- 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
- Garth Warner, Harmonic analysis on semi-simple Lie groups. I, Die Grundlehren der mathematischen Wissenschaften, Band 188, Springer-Verlag, New York-Heidelberg, 1972. MR 0498999
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 61 (1976), 131-136
- MSC: Primary 22C05; Secondary 22D12
- DOI: https://doi.org/10.1090/S0002-9939-1976-0430144-6
- MathSciNet review: 0430144