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An irreducible unitary representation of a compact group is finite dimensional. (English) Zbl 0079.32802


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[1] Anna Hurevitsch, Unitary representation in Hilbert space of a compact topological group, Rec. Math. [Mat. Sbornik] N. S. 13(55) (1943), 79 – 86 (English, with Russian summary). · Zbl 0061.25403
[2] L. Pontrjagin, Topological groups, Princeton University Press, 1946. · JFM 62.0443.02
[3] I. Gelfand and D. Raikov, Irreducible unitary representations of locally bicompact groups, Rec. Math. [Mat. Sbornik] N. S. 13(55) (1943), 301 – 316. · Zbl 0063.01566
[4] Henri Cartan and Roger Godement, Théorie de la dualité et analyse harmonique dans les groupes abéliens localement compacts, Ann. Sci. École Norm. Sup. (3) 64 (1947), 79 – 99 (French). · Zbl 0033.18801
[5] Lynn H. Loomis, An introduction to abstract harmonic analysis, D. Van Nostrand Company, Inc., Toronto-New York-London, 1953. · Zbl 0052.11701
[6] Einar Hille, Functional Analysis and Semi-Groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, New York, 1948. · Zbl 0033.06501
[7] Béla v. Sz. Nagy, Spektraldarstellung linearer Transformationen des Hilbertschen Raumes, Ergebnisse der Mathematik und ihrer Grenzgebiete, 5, no. 5, Springer, Berlin, 1942 (German). · JFM 68.0241.01
[8] S. Banach, Théorie des opérations linéaires, Warsaw, Monografje Mat., 1932. · JFM 58.0420.01
[9] Seminaire Sophus Lie, École Normale Supérieure, Paris, 1955.
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