The Soft Torus II: A Variational Analysis of Commutator Norms
funct-an
2008-02-03 v1 Operator Algebras
Abstract
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.
Cite
@article{arxiv.funct-an/9212004,
title = {The Soft Torus II: A Variational Analysis of Commutator Norms},
author = {Ruy Exel},
journal= {arXiv preprint arXiv:funct-an/9212004},
year = {2008}
}
Comments
14 pages, plain TeX, UNM-RE-003