On the Fourier-algebra of a locally compact amenable group

P-Amenable Locally Compact Hypergroups

p-amenable locally compact hypergroups

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Fourier and Figà-Talamanca–Herz algebras on amenable, locally compact groups

For a locally compact group G, let A(G) denote its Fourier algebra and, for p ∈ (1,∞), let Ap(G) be the corresponding Figà-Talamanca–Herz algebra. For amenable G and p, p ∈ (1,∞) such that 1 p + 1 p , we show that Ap(G) ∩Ap′(G) = A(G).

SPECTRUM OF THE FOURIER-STIELTJES ALGEBRA OF A SEMIGROUP

For a unital foundation topological *-semigroup S whose representations separate points of S, we show that the spectrum of the Fourier-Stieltjes algebra B(S) is a compact semitopological semigroup. We also calculate B(S) for several examples of S.

An Amenable Group with a Nonsymmetric Group Algebra

Let G be a discrete group, h(G) the group algebra of G. Symmetry of h(G) has been considered in [l], [3]. Groups containing a free subgroup on two or more generators are the only groups found to have nonsymmetric group algebras, and in each case the groups found to have symmetric algebras are in the family of amenable groups. In this note we present an example of an amenable group with a nonsym...