arXiv math/01102942001-10-26math.DGmath.OA

A semicontinuous trace for almost local operators on an open manifold

Daniele Guido, Tommaso Isola

备注：: 17 pages, to appear on the International Journal of mathematics. This paper roughly correspond to the first section of the unpublished preprint math.DG/9809040
发表信息：: Internat. J. Math. 12, (2001) 1087-1102
DOI：: 10.1142/S0129167X01001106

英文摘要：

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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