Almost commuting unitary elements in purely infinite simple \(C^*\)- algebras (Q1906492)

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 \(|v- V|< \varepsilon\).