Equality of three numerical radius inequalities

Hwa Long Gau; Pei Yuan Wu

doi:10.1016/j.laa.2018.05.021

Equality of three numerical radius inequalities

Hwa Long Gau, Pei Yuan Wu

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

4 引文斯高帕斯（Scopus）

摘要

For an n-by-n matrix A, let w(A) and ‖A‖ denote its numerical radius and operator norm, respectively. The following three inequalities, each a strengthening of w(A)≤‖A‖, are known to hold: w(A)²≤(‖A‖²+w(A²))/2, w(A)≤(‖A‖+‖A²‖^1/2)/2, and w(A)≤(‖A‖+w(Δ_t(A)))/2 (0≤t≤1), where Δ_t(A) is the generalized Aluthge transform of A. In this paper, we derive necessary and sufficient conditions in terms of the operator structure of A for which the inequalities become equalities.

原文	???core.languages.en_GB???
頁（從 - 到）	51-67
頁數	17
期刊	Linear Algebra and Its Applications
卷	554
DOIs	https://doi.org/10.1016/j.laa.2018.05.021
出版狀態	已出版 - 1 10月 2018

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10.1016/j.laa.2018.05.021

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AU - Gau, Hwa Long

AU - Wu, Pei Yuan

PY - 2018/10/1

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N2 - For an n-by-n matrix A, let w(A) and ‖A‖ denote its numerical radius and operator norm, respectively. The following three inequalities, each a strengthening of w(A)≤‖A‖, are known to hold: w(A)2≤(‖A‖2+w(A2))/2, w(A)≤(‖A‖+‖A2‖1/2)/2, and w(A)≤(‖A‖+w(Δt(A)))/2 (0≤t≤1), where Δt(A) is the generalized Aluthge transform of A. In this paper, we derive necessary and sufficient conditions in terms of the operator structure of A for which the inequalities become equalities.

AB - For an n-by-n matrix A, let w(A) and ‖A‖ denote its numerical radius and operator norm, respectively. The following three inequalities, each a strengthening of w(A)≤‖A‖, are known to hold: w(A)2≤(‖A‖2+w(A2))/2, w(A)≤(‖A‖+‖A2‖1/2)/2, and w(A)≤(‖A‖+w(Δt(A)))/2 (0≤t≤1), where Δt(A) is the generalized Aluthge transform of A. In this paper, we derive necessary and sufficient conditions in terms of the operator structure of A for which the inequalities become equalities.

KW - Generalized Aluthge transform

KW - Numerical radius

KW - Numerical range

KW - Operator norm

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M3 - 期刊論文

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JO - Linear Algebra and Its Applications

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ER -

Equality of three numerical radius inequalities

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