In this short note we first extend the validity of the spectral radius formula obtained in \cite{ag} to 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 non-trivial constraints between 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 Haar measure.

中文翻译：

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傅里叶-斯蒂尔杰斯代数的光谱半径公式

在这个简短的注释中，我们首先将在 \cite{ag} 中获得的谱半径公式的有效性扩展到傅里叶 - Stieltjes 代数。第二部分致力于证明对于任何局部紧非离散阿贝尔群上的测度代数，三个量之间没有非平凡的约束：范数、谱半径和傅里叶-斯蒂尔杰斯变换的上限值，即使我们将注意力限制在所有卷积幂相对于 Haar 度量都是奇异的度量上。