Smale空间中C ~*-代数的迹渐近性
Trace Asymptotics for C*-Algebras from Smale Spaces
摘要：
我们考虑在双曲动力系统Smale空间中与稳定和不稳定等价相关的C*-代数。这些系统包括有限型的移位，在这种情况下，这些C*-代数都是AF-代数。这些代数在一个单一的希尔伯特空间上有基本的表示（取决于周期点的选择），它有许多特殊的性质。特别地，第一个代数的任何元素与第二个代数的任何元素之间的乘积是紧的。此外，还有一个单一的酉算子，它实现了对两者的操作。在这里，在系统是混合的假设下，我们证明了这些代数上的（半有限）迹可以通过一个限制过程和通常的算子迹得到。
英文摘要：
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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