Almost commuting unitaries with spectral gap are near commuting unitaries
| dc.creator | Osborne, Tobias J. | |
| dc.date | 2008-09-03 | |
| dc.date.accessioned | 2026-07-07T10:00:20Z | |
| dc.date.available | 2026-07-07T10:00:20Z | |
| dc.description | Let M_n be the collection of n x n complex matrices equipped with operator norm. Suppose U, V \in M_n are two unitary matrices, each possessing a gap larger than Δin their spectrum, which satisfy ||UV-VU|| \le ε. Then it is shown that there are two unitary operators X and Y satisfying XY-YX = 0 and ||U-X|| + ||V-Y|| \le E(Δ^2/ε) (ε/Δ^2)^(1/6), where E(x) is a function growing slower than x^(1/k) for any positive integer k. | |
| dc.description | 5 pages | |
| dc.identifier | https://arxiv.org/abs/0809.0602 | |
| dc.identifier | http://arxiv.org/abs/0809.0602 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168297 | |
| dc.subject | Operator Algebras | |
| dc.subject | Mathematical Physics | |
| dc.subject | Quantum Physics | |
| dc.subject | 15A15, 15A27, 47A55; 47B47 | |
| dc.title | Almost commuting unitaries with spectral gap are near commuting unitaries | |
| dc.type | text |