most recent 30 from http://mathoverflow.net 2013-05-20T06:03:13Z http://mathoverflow.net/feeds/question/16813 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/16813/obstructions-to-existence-of-finitely-summable-spectral-triples Kamran Reihani 2010-03-02T01:33:02Z 2011-02-26T21:14:46Z

<p>Connes proved in his beautiful paper "Compact metric spaces, Fredholm modules, and hyperfiniteness" published in 1989 that if $(A,H,D)$ is a finitely summable spectral triple with a unital <code>$C^*$</code>-algebra $A$, then $A$ must have a tracial state. Here is the question: Is there an analogue of this result for non-unital spectral triples (for which $A$ is a non-unital <code>$C^*$</code>-algebra and $D$ has locally compact resolvents)? What are the main obstructions for existence of finitely summable spectral triples?</p>