Multipliers and asymptotic behaviour of the Fourier algebra of nonamenable groups
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- by Claudio Nebbia
- Proc. Amer. Math. Soc. 84 (1982), 549-554
- DOI: https://doi.org/10.1090/S0002-9939-1982-0643747-3
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Abstract:
Let $G$ be a locally compact group and $A(G)$ the algebra of matrix coefficients of the regular representation. We prove that $G$ is amenable if and only if there exist functions $u \in A(G)$ which vanish at infinity at any arbitrarily slow rate. The "only if" part of the result was essentially known. With the additional hypothesis that $G$ be discrete, we deduce that $G$ is amenable if and only if every multiplier of the algebra $A(G)$ is a linear combination of positive definite functions. Again, the "only if" part of this result was known.References
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Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 549-554
- MSC: Primary 43A07; Secondary 43A30
- DOI: https://doi.org/10.1090/S0002-9939-1982-0643747-3
- MathSciNet review: 643747