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

Department of Mathematics

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

Abstract

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].

Original language	English
Pages (from-to)	258-281
Number of pages	24
Journal	Linear Algebra and Its Applications
Volume	533
DOIs	https://doi.org/10.1016/j.laa.2017.07.024
State	Published - 15 Nov 2017

Keywords

Commutator
Jordan product
Numerical radius

Access to Document

10.1016/j.laa.2017.07.024

Cite this

@article{e65181d1438949bba26e44a79d6f25cf,

title = "Extremality of numerical radii of matrix commutators and Jordan products",

abstract = "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].",

keywords = "Commutator, Jordan product, Numerical radius",

author = "Gau, {Hwa Long} and Wang, {Kuo Zhong}",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

month = nov,

day = "15",

doi = "10.1016/j.laa.2017.07.024",

language = "???core.languages.en_GB???",

volume = "533",

pages = "258--281",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

}

TY - JOUR

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

UR - http://www.scopus.com/inward/record.url?scp=85026677899&partnerID=8YFLogxK

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

Abstract

Keywords

Access to Document

Fingerprint

Cite this