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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
    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
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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