Let G be a locally compact abelian group, and let p 2 1; 1). We show that the Segal algebra S p (G) is always weakly amenable, but that it is amenable only if G is discrete.

It is shown that the convergence of convolution products of probability measures on certain non-locally compact topological abelian groups can be verified by means of characteristic functionals. Analogous results are obtained also for almost everywhere convergence of series of independent random elements in the considered groups. A connection with the Sazonov property of the groups is discussed...

Let G be a locally compact, σ-compact group. We prove that the equivariant KK-theory, KK, is the universal category for functors from G-algebras to abelian groups which are stable, homotopy invariant and split-exact. This is a generalization of Higsons characterisation of (non-equivariant) KK-theory.

The Fourier and Fourier-Stieltjes algebras A(G) and B(G) of a locally compact group G are introduced and studied in 60’s by Piere Eymard in his PhD thesis. If G is a locally compact abelian group, then A(G) ≃ L(Ĝ), and B(G) ≃ M(Ĝ), via the Fourier and Fourier-Stieltjes transforms, where Ĝ is the Pontryagin dual of G. Recently these algebras are defined on a (topological or measured) groupoid an...

The well-known duality theorem of Pontryagin and van Kampen [27, 20] states that the characters of an Abelian locally compact group G also form a group Ĝ, and the group of characters of Ĝ is isomorphic to G. For non-Abelian groups, there is no such duality. In a few words, difficulties on this way arise from the fact that the dual space of a noncommutative group, however defined, has no natural...

in this paper, we investigate the relation between l-projections and conditional expectations on subalgebras of the fourier-stieltjes algebra b(g), and we will show that compactness of g plays an important role in this relation.

Suppose that y is a continuous homomorphism of a locally compact group G into another such group, H, then ¡p induces in a natural way a homomorphism 9>* of the measure algebra of G, called M(G), into M(H). The action of <p* on the subspace M0(G) is studied in this paper. The space M0(G) is the nonabelian analogue to the space of measures on a locally compact abelian group whose Fourier-Stieltje...