The Spectral Radius Formula for Fourier-Stieltjes Algebras

Journal article, 2020

In this short note we first extend the validity of the spectral radius formula, obtained by M. Anoussis and G. Gatzouras, for Fourier-Stieltjes algebras. The second part is devoted to showing that, for the measure algebra on any locally compact non-discrete Abelian group, there are no nontrivial constraints among three quantities: the norm, the spectral radius, and the supremum of the Fourier-Stieltjes transform, even if we restrict our attention to measures with all convolution powers singular with respect to the Haar measure.