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 , 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.