We introduce the Fourier-Stieltjes algebra in Rn which we denote by FS(Rn). It is a subalgebra of the algebra of bounded uniformly continuous functions in Rn, BUC(Rn), strictly containing the almost periodic functions, whose elements are invariant by translations and possess a mean-value. Thus, it is a so called algebra with mean value, a concept introduced by Zhikov and Krivenko (1986). Namely...

Abstract. For any finite unital commutative idempotent semigroup S, a unital semilattice, we show how to compute the amenability constant of its semigroup algebra l(S), which is always of the form 4n+1. We then show that these give lower bounds to amenability constants of certain Banach algebras graded over semilattices. Our theory applies to certain natural subalgebras of Fourier-Stieltjes alg...

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.

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.

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.

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 ...

For locally compact groups Gi, i = 1, 2, · · · , n, let CB(G1, · · · , Gn) denote the Banach space of completely bounded multilinear forms on C0(G1)×· · ·×C0(Gn) in the completely bounded norm. CB(G1, · · · , Gn) has the structure of a Banach ∗-algebra under a multiplication and adjoint operation which agree with the convolution structure on the measure algebra M(G1 ×· · ·×Gn). If the Gi are al...

For a locally compact abelian group $G$, J. L. Taylor (1971) gave complete characterization of invertible elements in the measure algebra $M(G)$. Using Fourier-Stieltjes transform, this can be carried out context algebras $B(G)$. We obtain latter for $B(G)$ certain classes groups, particular, many totally minimal groups and $ax+b$-group.