Let \(X\) be a bounded geometry discrete metric space. Guoliang Yu defined a *ghost* to be an element of the Roe algebra \( C^*_u(X) \) that is given by a matrix \(T_{xy}\) whose entries tend to zero as \(x,y\to\infty\).

The original counterexamples of Higson to the coarse Baum-Connes conjecture were noncompact ghost projections on box spaces derived from property T groups. On the other hand, all ghost operators on a property A space are compact.

In *Ghostbusting and Property A*, Rufus Willett and I show that all ghosts on \(X\) are compact *if and only if* \(X\) has property A. (Appropriately enough, on a space without property A we construct ghosts using the spectral theorem.) The paper will appear in the *Journal of Functional Analysis*.

**Question:** To what characterization of ordinary amenability does this correspond?