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 provide necessary and sufficient conditions for the existence of idempotents arbitrarily large norm in Fourier algebra $A(G)$ Fourier–Stieltjes $B(G)$ a locally compact group $G$. prove that

For locally compact groups, Fourier algebras and Fourier-Stieltjes algebras have proved to be useful dual objects. They encode the representation theory of the group via the positive deenite functions on the group: positive deenite functions correspond to cyclic representations and span these algebras as linear spaces. They encode information about the algebra of the group in the geometry of th...

We announce the definition of the dual group, GB(^, of the Fourier-Stieltjes algebra, B(G), of a locally compact group G; and we state four main theorems culminating in the result that GB(G) is a locally compact topological group which is topological^ isomorphic to G. This result establishes an explicit dual relationship between a group and its Fourier-Stieltjes algebra. Moreover, this result e...

In this paper, some known results about the functorial properties of Fourier–Stieltjes algebra, B(G), will be generalized. First all, idempotent theorem on algebra promoted and linked to p-analog one. Next, $$\pi$$ -Fourier space introduced by Arsac given, taking advantage theory ultrafilters, connection between dual p-pseudofunctions fully investigated. As main result, one significant applicab...