Equality of three numerical radius inequalities

Hwa Long Gau, Pei Yuan Wu

研究成果: 雜誌貢獻期刊論文同行評審

2 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‖+‖A21/2)/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.

原文???core.languages.en_GB???
頁(從 - 到)51-67
頁數17
期刊Linear Algebra and Its Applications
554
DOIs
出版狀態已出版 - 1 10月 2018

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