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arXiv · 1208.5013

Trace Asymptotics for C*-Algebras from Smale Spaces

D. Brady Killough·Ian F. Putnam
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Abstract

We consider C*-algebras associated with stable and unstable equivalence in hyperbolic dynamical systems known as Smale spaces. These systems include shifts of finite type, in which case these C*-algebras are both AF-algebras. These algebras have fundamental representations on a single Hilbert space (subject to a choice of periodic points) which have a number of special properties. In particular, the product between any element of the first algebra with one from the second is compact. In addition, there is a single unitary operator which implements actions on both. Here, under the hypothesis that the system is mixing, we show that the (semi-finite) traces on these algebras may be obtained through a limiting process and the usual operator trace.

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D. Brady Killough, Ian F. Putnam. 2012-08-24. Trace Asymptotics for C*-Algebras from Smale Spaces. https://arxiv.org/abs/1208.5013

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