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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Properties of the Fourier algebra that are equivalent to amenability


Author: Viktor Losert
Journal: Proc. Amer. Math. Soc. 92 (1984), 347-354
MSC: Primary 43A22
DOI: https://doi.org/10.1090/S0002-9939-1984-0759651-8
MathSciNet review: 759651
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Abstract: It is shown that a locally compact group $ G$ is amenable iff each multiplier on the Fourier algebra $ A\left( G \right)$ is given by a function from the Fourier-Stieltjes algebra $ B\left( G \right)$. Another condition is that the norm of $ A\left( G \right)$ is equivalent to that induced by the regular representation of $ A\left( G \right)$.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0759651-8
Keywords: Locally compact groups, amenability, Fourier algebra, multipliers
Article copyright: © Copyright 1984 American Mathematical Society