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Almost commuting unitary elements in purely infinite simple \(C^*\)- algebras. (English) Zbl 0835.46054
It is shown that, for any \(\varepsilon> 0\), there exists \(\delta> 0\) such that for any pair of unitaries (selfadjoints), \(u\), \(v\) in any purely infinite simple \(C^*\)-algebra \(A\), if \(|uv- vu|< \delta\), then there exists a pair of commuting unitaries (selfadjoints) \(U\), \(V\in A\) satisfying \(|u- U|< \varepsilon\) and \(|v- V|< \varepsilon\).

MSC:
46L05 General theory of \(C^*\)-algebras
46L80 \(K\)-theory and operator algebras (including cyclic theory)
47C15 Linear operators in \(C^*\)- or von Neumann algebras
15A15 Determinants, permanents, traces, other special matrix functions
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