Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-25T03:01:36.508Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite dimensional submodules of G-modules for a compact group G

Published online by Cambridge University Press:  24 October 2008

Karl Heinrich Hofmann
Karl Heinrich Hofmann
Affiliation:
Tulane University
Get access Rights & Permissions [Opens in a new window]

Extract

We propose an exceptionally short and effortless approach to the fundamental facts of the representation theory of compact groups on Hilbert spaces and expand our methods to prove some generalizations concerning representations on arbitrary locally convex vector spaces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 1 , January 1969 , pp. 47 - 52
Copyright
Copyright © Cambridge Philosophical Society 1969

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bourbaki, N.Espaces vectoriels topologiques, Chapters I, II. (Paris, Hermann, 1953).Google Scholar
(2)Bourbaki, N.Integration, Chapters I-VIII (Paris, Hermann, 1952–1963).Google Scholar
(3)Chevalley, C.Theory of Lie groups (Princeton University Press, 1946).Google Scholar
(4)Dixmier, J.Les C*-algèbres et leurs représentations (Paris, Gautheir-Villars, 1964).Google Scholar
(5)Halmos, P. R.Measure theory (Princeton, Van Nostrand, 1950).CrossRefGoogle Scholar
(6)Hewitt, E. and Ross, K. A.Abstract harmonic analysis (Berlin, Springer, 1963).Google Scholar
(7)Hochschild, G.The structure of Lie groups (San Francisco, Holden-Day, 1965).Google Scholar
(8)Hussain, T.Introduction to topological groups (Philadelphia, Saunders, 1966).Google Scholar
(9)Loomis, L. H.An introduction to abstract harmonic analysis (Princeton, Van Nostrand, 1953).Google Scholar
(10)Montgomery, D. and Zippin, L.Topological transformation groups (New York, Interscience, 1955).Google Scholar
(11)Naimark, M. A.Normed rings (Moscow, 1956).Google Scholar
(12)Pontryagin, A. S.Topological groups (Moscow, 2nd ed., 1953).Google Scholar
(13)Schaefer, H. H.Topological vector spaces (New York, Macmillan, 1966).Google Scholar
(14)Séminaire Sophus Lie (Paris, École Norm. Sup., 1955).Google Scholar
(15)Weil, A.L'intégration dans les groupes topologiques (Paris, Hermann, 1953).Google Scholar
(16)Glicksberg, I. and de Leeuw, K.Applications of almost periodic compactifications. Acta. Math. 105 (1961), 63–97.Google Scholar
(17)Glicksberg, I. and de Leeuw, K.The decomposition of certain group representations. J. Analyse Math. 15 (1965), 135–192.Google Scholar
(18)Hofmann, K. H.Zerfällung topologischer Gruppen. Math. Z. 84 (1964), 16–37.CrossRefGoogle Scholar
(19)Rudin, W.Projections on invariant subspaces. Proc. Amer. Math. Soc. 13 (1962), 429–432.CrossRefGoogle Scholar
(20)Shiga, K.Representation of a compact group on a Banach space. J. Math. Soc. Japan 7 (1955), 224–248.Google Scholar