A semicontinuous trace for almost local operators on an open manifold
Daniele Guido, Tommaso Isola
Abstract
A semicontinuous semifinite trace is constructed on the C*-algebra generated by the finite propagation operators acting on the L2-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).
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