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.

Returning to a classical question in Harmonic Analysis we strengthen an old result of Walter Rudin. We show that there exists a weakly almost periodic function on the group of integers Z which is not in the norm-closure of the algebra B(Z) of Fourier-Stieltjes transforms of measures on the dual group Ẑ = T, and which is recurrent. We also show that there is a Polish monothetic group which is re...

Let (G,tau_G) be a topological group. We establish relationships between weakly almost periodic topologies on G coarser than tau_G, central idempotents in the compactification G^W, and certain ideals algebra of functions W(G). gain decompositions representations, generalizing many from literature. look at role pre-locally compact topologies, unitarizable extend or to Fourier-Stieltjes algebras ...

Let G be a locally compact σ-compact group. Motivated by an earlier notion for discrete groups due to Effros and Ruan, we introduce the multidimensional Fourier algebra A(G) of G. We characterise the completely bounded multidimensional multipliers associated with A(G) in several equivalent ways. In particular, we establish a completely isometric embedding of the space of all n-dimensional compl...

We study a generalisation of operator spaces modelled on Lp spaces, instead of Hilbert spaces, using the notion of p-complete boundedness, as studied by Pisier and Le Merdy. We show that the Figà-Talamanca-Herz Algebras Ap(G) becomes quantised Banach algebras in this framework, and that the cohomological notion of amenability of these algebras corresponds to amenability of the locally compact 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 ...