UM
On some norm inequalities involving the commutator and XY - YXT
Cheng,Che Man1; Fong,Kin Sio2; Lei,Weng Fai1
2013-03-15
Source PublicationLinear Algebra and Its Applications
ISSN0024-3795
Volume438Issue:6Pages:2793-2807
AbstractLet X and Y be any n × n complex matrices, ∥ ·∥ be the Frobenius norm and ∥·∥ be the (2,2)-norm defined by ∥X∥=s (X)+s(X), where s (X)≥⋯≥ sn are the singular values of X. Based on the paper [A. Böttcher and D. Wenzel, The Frobenius norm and the commutator, Linear Algebra Appl. 429 (2008) 1864-1885], a common approach is found for proving the following three inequalities: ∥XY-YX∥ ≤ √2∥X∥∥Y∥, ∥XY-YX∥≤ √2∥X∥ ∥Y∥and∥XY- YX∥≤ √2∥X∥∥Y∥ . The first two are known and the third one is new. Their equality cases are also determined. In particular it is found that, while there are common analogous equality cases, the third inequality admits an equality case that the other two do not have as a corresponding counterpart. © 2012 Elsevier Inc. All rights reserved.
KeywordCommutator Norm inequality
DOI10.1016/j.laa.2012.11.007
URLView the original
Language英语
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Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.Department of Mathematics,University of Macau,Macao
2.Department of Finance and Business Economics,University of Macau,Macao
First Author AffilicationUniversity of Macau
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GB/T 7714
Cheng,Che Man,Fong,Kin Sio,Lei,Weng Fai. On some norm inequalities involving the commutator and XY - YXT[J]. Linear Algebra and Its Applications,2013,438(6):2793-2807.
APA Cheng,Che Man,Fong,Kin Sio,&Lei,Weng Fai.(2013).On some norm inequalities involving the commutator and XY - YXT.Linear Algebra and Its Applications,438(6),2793-2807.
MLA Cheng,Che Man,et al."On some norm inequalities involving the commutator and XY - YXT".Linear Algebra and Its Applications 438.6(2013):2793-2807.
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