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Another unitarily invariant norm attaining the minimum norm bound for commutators
Kin-Sio Fong; Che-Man Cheng; Io-Kei Lok
2010-12-30
Source PublicationLinear Algebra and Its Applications
ISSN0024-3795
Volume433Issue:11-12Pages:1793-1797
Abstract

Böttcher and Wenzel recently proved that for any unitarily invariant norm ∥· ∥, sup ∥XY-YX∥/ ∥XY∥ ∥X and aren×nnon-zero complex matrices=C≥2 and that C=2 when the norm is the Frobenius norm. They also asked whether the Frobenius norm is the only one having such property. In this paper, we answer the question by showing that the dual norm of the (2,2)-norm also has the property that C=2½

KeywordCommutator Norm Inequality Unitarily Invariant Norm
DOIhttps://doi.org/10.1016/j.laa.2010.06.037
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000283893700008
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被引频次[WOS]:5   [WOS记录]     [WOS相关记录]
Document TypeJournal article
专题DEPARTMENT OF MATHEMATICS
Corresponding AuthorKin-Sio Fong
AffiliationDepartment of Mathematics, University of Macau, Macao, China
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
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Kin-Sio Fong,Che-Man Cheng,Io-Kei Lok. Another unitarily invariant norm attaining the minimum norm bound for commutators[J]. Linear Algebra and Its Applications,2010,433(11-12):1793-1797.
APA Kin-Sio Fong,Che-Man Cheng,&Io-Kei Lok.(2010).Another unitarily invariant norm attaining the minimum norm bound for commutators.Linear Algebra and Its Applications,433(11-12),1793-1797.
MLA Kin-Sio Fong,et al."Another unitarily invariant norm attaining the minimum norm bound for commutators".Linear Algebra and Its Applications 433.11-12(2010):1793-1797.
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