Compact metric spaces, Fredholm modules, and hyperfiniteness

1 June 1989

journal article
research article
Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems

Vol. 9 (2) , 207-220
https://doi.org/10.1017/s0143385700004934

Abstract

We show that the existence of a finitely summable unbounded Fredholm module (h, D) on a C* algebra A implies the existence of a trace state on A and that no such module exists on the C* algebra of a non amenable discrete group. Both for the needs of non commutative differential geometry and of analysis in infinite dimension we are led to the better notion of the θ-summable Fredholm module.

Keywords

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