Abstract.
Let G be a locally compact group. We show that its Fourier algebra A(G) is amenable if and only if G has an abelian subgroup of finite index, and that its Fourier–Stieltjes algebra B(G) is amenable if and only if G has a compact, abelian subgroup of finite index. We then show that A(G) is weakly amenable if the component of the identity of G is abelian, and we prove some partial results towards the converse.
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Research supported by NSERC under grant no. 90749-00.
Research supported by NSERC under grant no. 227043-00.
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Forrest, B., Runde, V. Amenability and weak amenability of the Fourier algebra. Math. Z. 250, 731–744 (2005). https://doi.org/10.1007/s00209-005-0772-2
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DOI: https://doi.org/10.1007/s00209-005-0772-2