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.
Guido, D., Isola, T. (2001). A semicontinuous trace for almost local operators on an open manifold. INTERNATIONAL JOURNAL OF MATHEMATICS, 12(9), 1087-1102 [10.1142/S0129167X01001106].
A semicontinuous trace for almost local operators on an open manifold
GUIDO, DANIELE;ISOLA, TOMMASO
2001-01-01
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.File in questo prodotto:
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