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A semicontinuous trace for almost local operators on an open manifold

Daniele Guido·Tommaso Isola
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Abstract

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).

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Daniele Guido, Tommaso Isola. 2001-10-26. A semicontinuous trace for almost local operators on an open manifold. https://doi.org/10.1142/s0129167x01001106

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