On the structure of invertible elements in certain Fourier–Stieltjes algebras

Abstract

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