Averaging a representation over a subgroup
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- by R. B. Burckel PDF
- Proc. Amer. Math. Soc. 78 (1980), 399-402 Request permission
Abstract:
The purpose of this note is to extend a well-known 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 (Ryll-Nardzewski [5]).References
- R. B. Burckel, Weakly almost periodic functions on semigroups, Gordon and Breach Science Publishers, New York-London-Paris, 1970. MR 0263963
- Ching Chou, Uniform closures of Fourier-Stieltjes algebras, Proc. Amer. Math. Soc. 77 (1979), no. 1, 99–102. MR 539638, DOI 10.1090/S0002-9939-1979-0539638-9
- W. F. Eberlein, Abstract ergodic theorems and weak almost periodic functions, Trans. Amer. Math. Soc. 67 (1949), 217–240. MR 36455, DOI 10.1090/S0002-9947-1949-0036455-9
- Pierre Eymard, L’algèbre de Fourier d’un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181–236 (French). MR 228628
- Czesław Ryll-Nardzewski, On fixed points of semigroups of endomorphisms of linear spaces, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66) Univ. California Press, Berkeley, Calif., 1967, pp. 55–61. MR 0215134
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 78 (1980), 399-402
- MSC: Primary 22D10; Secondary 43A07
- DOI: https://doi.org/10.1090/S0002-9939-1980-0553383-3
- MathSciNet review: 553383