Ordered invariant ideals of Fourier-Stieltjes algebras

Abstract

In a recent paper on exotic crossed products, we included a lemma concerning ideals of the Fourier-Stieltjes algebra. Buss, Echterhoff, and Willett have pointed out to us that our proof of this lemma contains an error. In fact, it remains an open question whether the lemma is true as stated. In this note we indicate how to contain the resulting damage. Our investigation of the above question leads us to define two properties \emph{ordered} and \emph{weakly ordered} for invariant ideals of Fourier-Stieltjes algebras, and we initiate a study of these properties.