Almost commuting unitaries with spectral gap are near commuting unitaries

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Tobias J. Osborne

External Research Organisations

  • Royal Holloway University of London
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Details

Original languageEnglish
Pages (from-to)4043-4048
Number of pages6
JournalProceedings of the American Mathematical Society
Volume137
Issue number12
Publication statusPublished - 7 Aug 2009
Externally publishedYes

Abstract

Let Mn be the collection of n × n complex matrices equipped with operator norm. Suppose U, V ∈ Mn are two unitary matrices, each possessing a gap larger than Δ in their spectrum, which satisfy ∥UV - VU∥ ≤ ε. Then it is shown that there are two unitary operators X and Y satisfying XY-YX = 0 and ∥U -X∥+∥V -Y∥ ≤ E(Δ2/ε) (ε/Δ2)1/6, where E(x) is a function growing slower than x1/k for any positive integer k.

ASJC Scopus subject areas

Cite this

Almost commuting unitaries with spectral gap are near commuting unitaries. / Osborne, Tobias J.
In: Proceedings of the American Mathematical Society, Vol. 137, No. 12, 07.08.2009, p. 4043-4048.

Research output: Contribution to journal › Article › Research › peer review

Osborne TJ. Almost commuting unitaries with spectral gap are near commuting unitaries. Proceedings of the American Mathematical Society. 2009 Aug 7;137(12):4043-4048. doi: 10.1090/S0002-9939-09-10026-6
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