The Dual Group of the Fourier-stieltjes Algebra
نویسندگان
چکیده
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 extends naturally the notion of Pontriagin duality to the case of noncommutative groups. 1. We shall adopt the notation and assume familiarity with the results of [3], [4]. We recall from [3], [4] that each e Aut(£(G)), the isometric algebra automorphisms of the Banach algebra B(G), can be written in the form
منابع مشابه
Some notes on L-projections on Fourier-Stieltjes algebras
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.
متن کاملSPECTRUM 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.
متن کاملFourier-stieltjes Algebras of Locally Compact Groupoids
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...
متن کاملRepresentations of locally compact groups on QSLp-spaces and a p-analog of the Fourier–Stieltjes algebra
For a locally compact group G and p ∈ (1,∞), we define Bp(G) to be the space of all coefficient functions of isometric representations of G on quotients of subspaces of Lp spaces. For p = 2, this is the usual Fourier–Stieltjes algebra. We show that Bp(G) is a commutative Banach algebra that contractively (isometrically, if G is amenable) contains the Figà-Talamanca–Herz algebra Ap(G). If 2 ≤ q ...
متن کاملThe Restricted Algebras on Inverse Semigroups Iii, Fourier Algebra
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...
متن کامل