  A semicontinuous semifinite trace is constructed on the C*-algebra generated
by the finite propagation operators acting on the L^2-sections of a hermitian
vector bundle on an amenable open manifold of bounded geometry. This trace is
the semicontinuous regularization of a functional already considered by J. Roe.
As an application, we show that, by means of this semicontinuous trace,
Novikov-Shubin numbers for amenable manifolds can be defined (cf.
math.OA/9802015 for an alternate definition).
