Almost commuting self-adjoint matrices --- the real and self-dual cases

Details Almost commuting self-adjoint matrices --- the real and self-dual cases Almost commuting self-adjoint matrices --- the real and self-dual cases

2010-12-16

arxiv.org/abs/1012.3494v2

Mathematics

Operator Algebras

Expanded references. 33 pages

Scientific paper

We show that a pair of almost commuting self-adjoint, symmetric matrices are close to commuting self-adjoint, symmetric matrices (in a uniform way). Moreover we prove that the same holds with self-dual in place of symmetric. Since a symmetric, self-adjoint matrix is real, the former gives a real version of Huaxin Lin's famous theorem on almost commuting matrices. There are applications to physics of Lin's original theorem and both new cases. The self-dual case applies specifically to systems that respect time reversal. Along the way we develop some theory for semiprojective real C*-algebras.

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