The Soft Torus II: A Variational Analysis of Commutator Norms

Details The Soft Torus II: A Variational Analysis of Commutator Norms The Soft Torus II: A Variational Analysis of Commutator Norms

1992-12-19

arxiv.org/abs/funct-an/9212004v1

Mathematics

Operator Algebras

14 pages, plain TeX, UNM-RE-003

Scientific paper

The field of C*-algebras over the interval [0,2] for which the fibers are the Soft Tori is shown to be continuous. This result is applied to show that any pair of non-commuting unitary operators can be perturbed (in a weak sense) in such a way to decrease the commutator norm. Perturbations in norm are also considered and a characterization is given for pairs of unitary operators which are local minimum points for the commutator norm in the finite dimensional case.

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