Traces, Ultrapowers and the Pedersen-Petersen C*-Algebras
Traces, Ultrapowers and the Pedersen-Petersen C*-Algebras
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迹、超幂和 Pedersen-Petersen C* 代数
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
I. Farah
中科院分区：
文献类型：
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作者：
T. Bice;I. Farah
我们的动机问题是：是否C*-代数A的U-超幂上的所有迹必然是A上迹的U-极限，其中U是N上的非主超滤子。我们证明，只要A有无穷多个极值迹，甚至在超幂上显示出2^c大小的迹族，这是假的。对于这一点，即使当A有1000个迹时也失败意味着A包含可以表示为n+1的和的算子，但对于任意大的n，不能表示为n *-算子。我们证明了对于Pedersen-Petersen C ~*-代数的直和，这也会发生，并分析了这些C ~*-代数的其他一些有趣的性质。
Our motivating question was whether all traces on a U-ultrapower of a C*-algebra A, where U is a non-principal ultrafilter on N, are necessarily U-limits of traces on A. We show that this is false so long as A has infinitely many extremal traces, and even exhibit a 2^c size family of such traces on the ultrapower. For this to fail even when A has finitely many traces implies that A contains operators that can be expressed as sums of n+1 but not n *-commutators, for arbitrarily large n. We show that this happens for a direct sum of Pedersen-Petersen C*-algebras, and analyze some other interesting properties of these C*-algebras.
C* 代数的 Dixmier 近似和对称服从性。
DOI：
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发表时间：
2013
期刊：
J. Math. Sci. Univ. Tokyo
影响因子：
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作者：
Okibayashi;Y.;et al.;N. Ozawa; Dixmier approximation and symmetric amenability for C*-algebras.
通讯作者：
N. Ozawa; Dixmier approximation and symmetric amenability for C*-algebras.