Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Studia Mathematica / All issues

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.