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Existence and nonuniqueness of invariant means on $ \mathcal{L}^\infty(\hat G)$


Authors: Charles F. Dunkl and Donald E. Ramirez
Journal: Proc. Amer. Math. Soc. 32 (1972), 525-530
MSC: Primary 43A07; Secondary 46J99
DOI: https://doi.org/10.1090/S0002-9939-1972-0296609-1
MathSciNet review: 0296609
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Abstract: For G an infinite compact group we show the existence and nonuniqueness of invariant means on the dual of the Fourier algebra. It follows that the space of weakly almost periodic functionals on the Fourier algebra is a proper closed subspace of the dual of the Fourier algebra.


References [Enhancements On Off] (What's this?)

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  • [4] T. Mitchell, Constant functions and left invariant means on semigroups, Trans. Amer. Math. Soc. 119 (1965), 244-261. MR 33 #1743. MR 0193523 (33:1743)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0296609-1
Keywords: Invariant mean, weakly almost periodic functional, almost periodic functional, compact groups, Fourier algebra
Article copyright: © Copyright 1972 American Mathematical Society

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