The soft torus: A variational analysis of commutator norms (Q1891767)

The author shows that the field of \(C^*\)-algebras over the interval \([0, 2]\) for which the fibers are the soft tori is continuous. This result is applied to show that any pair of noncommuting unitary operators can be perturbed (in a weak sense) in a way which decreases the commutator norm. He also considers perturbations in the norm and gives a characterization for pairs of unitary operators which are local minimum points for the commutator norm in the finite-dimensional case.