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A semicontinuous trace for almost local operators on an open manifold | | Daniele Guido
; Tommaso Isola
; | | Date: |
26 Oct 2001 | | Journal: | Internat. J. Math. 12, (2001) 1087-1102 DOI: 10.1142/S0129167X01001106 | | Subject: | Differential Geometry; Operator Algebras MSC-class: 58-XX; 46Lxx | math.DG math.OA | | Affiliation: | U. Basilicata), Tommaso Isola (U. Roma Tor Vergata | | 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). | | Source: | arXiv, math.DG/0110294 | | Services: | Forum | Review | PDF | Favorites | |
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