We consider the Fourier-Stieltjes algebra $\mathrm{B}(G)$ of a locally compact group G. We show that operator amenability of $\mathrm{B}(G)$ implies that a certain semitopological compactification of G admits only finitely many idempotents. In the case that G is connected, we show that operator amenability of $\mathrm{B}(G)$ entails that G is compact.

中文翻译：

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傅里叶-Stieltjes代数的算符适用性

我们考虑傅立叶-Stieltjes代数 $\mathrm{乙}（G）$局部紧致群G的一个。我们显示出$\mathrm{乙}（G）$暗示G的某种半拓扑紧缩只允许有限的许多幂等。在连接了G的情况下，我们表明$\mathrm{乙}（G）$意味着G是紧凑的。