Extremality of numerical radii of matrix commutators and Jordan products

Hwa Long Gau; Kuo Zhong Wang

doi:10.1016/j.laa.2017.07.024

Extremality of numerical radii of matrix commutators and Jordan products

Hwa Long Gau, Kuo Zhong Wang

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研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

摘要

It is known that the numerical radius of the commutator (resp., Jordan product) AB−BA (resp., AB+BA) of two n-by-n matrices A and B is related to those of A and B by w(AB±BA)≤4w(A)w(B). In this paper, we give complete characterizations of A and B for which the equality is attained. The matrices involved can be considered as elaborate generalizations of the equality-attaining A=[0a00] and B=[00b0].

原文	???core.languages.en_GB???
頁（從 - 到）	258-281
頁數	24
期刊	Linear Algebra and Its Applications
卷	533
DOIs	https://doi.org/10.1016/j.laa.2017.07.024
出版狀態	已出版 - 15 11月 2017

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10.1016/j.laa.2017.07.024

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T1 - Extremality of numerical radii of matrix commutators and Jordan products

AU - Gau, Hwa Long

AU - Wang, Kuo Zhong

PY - 2017/11/15

Y1 - 2017/11/15

N2 - It is known that the numerical radius of the commutator (resp., Jordan product) AB−BA (resp., AB+BA) of two n-by-n matrices A and B is related to those of A and B by w(AB±BA)≤4w(A)w(B). In this paper, we give complete characterizations of A and B for which the equality is attained. The matrices involved can be considered as elaborate generalizations of the equality-attaining A=[0a00] and B=[00b0].

AB - It is known that the numerical radius of the commutator (resp., Jordan product) AB−BA (resp., AB+BA) of two n-by-n matrices A and B is related to those of A and B by w(AB±BA)≤4w(A)w(B). In this paper, we give complete characterizations of A and B for which the equality is attained. The matrices involved can be considered as elaborate generalizations of the equality-attaining A=[0a00] and B=[00b0].

KW - Commutator

KW - Jordan product

KW - Numerical radius

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U2 - 10.1016/j.laa.2017.07.024

DO - 10.1016/j.laa.2017.07.024

M3 - 期刊論文

AN - SCOPUS:85026677899

SN - 0024-3795

VL - 533

SP - 258

EP - 281

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Extremality of numerical radii of matrix commutators and Jordan products

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