On operator amenability of Fourier-Stieltjes algebras

Abstract

We consider the Fourier-Stieltjes algebra B(G) of a locally compact group G. We show that operator amenability of 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 B(G) entails that G is compact.