Almost commuting self-adjoint matrices --- the real and self-dual cases
Almost commuting self-adjoint matrices --- the real and self-dual cases
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几乎通勤自共矩阵——实数和自对偶情况
DOI：
10.1142/s0129055x16500173
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发表时间：
2010
影响因子：
1.8
通讯作者：
Adam P. W. Sørensen
中科院分区：
文献类型：
--
作者：
T. Loring;Adam P. W. Sørensen
我们证明了一对几乎可交换的自伴对称矩阵与一对可交换的自伴对称矩阵是一致的。此外，我们证明了同样适用于自对偶的地方对称的，也自共轭矩阵的道路。由于对称自伴矩阵是真实的，我们得到了林华新关于几乎可交换矩阵的著名定理的一个真实的版本。类似地，自对偶情形给出了四元数上的矩阵的一个版本。为了证明这些结果，我们发展了真实的C*-代数的半投射性理论，并研究了真实的C*-代数的低秩的各种定义。
We show that a pair of almost commuting self-adjoint, symmetric matrices is close to a pair of commuting self-adjoint, symmetric matrices (in a uniform way). Moreover, we prove that the same holds with self-dual in place of symmetric and also for paths of self-adjoint matrices. Since a symmetric, self-adjoint matrix is real, we get a real version of Huaxin Lin’s famous theorem on almost commuting matrices. Similarly, the self-dual case gives a version for matrices over the quaternions. To prove these results, we develop a theory of semiprojectivity for real C*-algebras and also examine various definitions of low-rank for real C*-algebras.