Averaging a representation over a subgroup
Author:
R. B. Burckel
Journal:
Proc. Amer. Math. Soc. 78 (1980), 399402
MSC:
Primary 22D10; Secondary 43A07
MathSciNet review:
553383
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Abstract: The purpose of this note is to extend a wellknown technique for getting a representation of a quotient group from one of the original group. This is usually done by ``integrating'' coefficient functions of the representation over the subgroup, i.e., by applying some mean to them. Hence amenability hypotheses are usually made. None are needed here because the relevant coefficient functions belong to the algebra of weakly almost periodic functions (Eberlein [3]), which is always amenable (RyllNardzewski [5]).
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R.
B. Burckel, Weakly almost periodic functions on semigroups,
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Ching
Chou, Uniform closures of FourierStieltjes
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Pierre
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Czesław
RyllNardzewski, On fixed points of semigroups of endomorphisms of
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 R. B. Burckel, Weakly almost periodic functions on semigroups, Gordon and Breach, New York, 1970. MR 0263963 (41:8562)
 [2]
 C. Chou, Uniform closures of FourierStieltjes algebras, Proc. Amer. Math. Soc. 77 (1979), 99102. MR 539638 (80i:43007)
 [3]
 W. F. Eberlein, Abstract ergodic theorems and weak almost periodic functions, Trans. Amer. Math. Soc. 67 (1949), 217240. MR 0036455 (12:112a)
 [4]
 P. Eymard, L'algèbre de Fourier d'un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181236. MR 0228628 (37:4208)
 [5]
 C. RyllNardzewski, On fixed points of semigroups of endomorphisms of linear spaces, Proc. of the Fifth Berkeley Sympos. on Mathematical Statistics and Probability (1965/66), vol. II, Part I: Theory of Probability, Univ. of California Press, Berkeley, 1967. MR 0215134 (35:5977)
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DOI:
http://dx.doi.org/10.1090/S00029939198005533833
PII:
S 00029939(1980)05533833
Keywords:
Unitary representation,
weakly almost periodic function,
mean value for WAP functions,
FourierStieltjes algebra (nonabelian)
Article copyright:
© Copyright 1980
American Mathematical Society
