Amenability properties of Fourier algebras and Fourier-Stieltjes algebras: a survey
نویسندگان
چکیده
منابع مشابه
Operator amenability of Fourier–Stieltjes algebras
In this paper, we investigate, for a locally compact groupG, the operator amenability of the Fourier-Stieltjes algebra B(G) and of the reduced Fourier-Stieltjes algebra Br(G). The natural conjecture is that any of these algebras is operator amenable if and only if G is compact. We partially prove this conjecture with mere operator amenability replaced by operator C-amenability for some constant...
متن کامل(Non-)amenability of Fourier and Fourier–Stieltjes algebras
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.
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We give an example of a non-compact, locally compact group G such that its Fourier–Stieltjes algebra B(G) is operator amenable. Furthermore, we characterize those G for which A * (G)—the spine of B(G) as introduced by M. Ilie and the second named author—is operator amenable and show that A * (G) is operator weakly amenable for each G.
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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.
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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...
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ژورنال
عنوان ژورنال: Banach Center Publications
سال: 2010
ISSN: 0137-6934,1730-6299
DOI: 10.4064/bc91-0-22