On the structure of invertible elements in certain Fourier–Stieltjes algebras
Volume 257 / 2021
Studia Mathematica 257 (2021), 347-360
MSC: Primary 43A30, 46J40; Secondary 43A70, 46M20.
DOI: 10.4064/sm200122-12-5
Published online: 22 September 2020
Abstract
For a locally compact abelian group $G$, J. L. Taylor (1972) 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.
