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TRACE ASYMPTOTICS FOR C*-ALGEBRAS FROM SMALE SPACES.
- Source :
- Proceedings of the American Mathematical Society; Jan2015, Vol. 143 Issue 1, p317-325, 9p
- Publication Year :
- 2015
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- HILBERT space
HOMEOMORPHISMS
HAUSDORFF spaces
PROOF theory
INVARIANT sets
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 143
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 99136916