The Soft Torus: A Variational Analysis of Commutator Norms
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 noncommuting unitary operators can be pertubed (in a weak sense) in a way which decreases the commutator norm. Perturbations in the norm...
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| Published in | Journal of functional analysis Vol. 126; no. 2; pp. 259 - 273 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.12.1994
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| Online Access | Get full text |
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| Summary: | 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 noncommuting unitary operators can be pertubed (in a weak sense) in a way which decreases the commutator norm. Perturbations in the 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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| ISSN: | 0022-1236 1096-0783 |
| DOI: | 10.1006/jfan.1994.1148 |