# Equality of three numerical radius inequalities

Hwa Long Gau, Pei Yuan Wu

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??? 51-67 17 Linear Algebra and Its Applications 554 https://doi.org/10.1016/j.laa.2018.05.021 已出版 - 1 10月 2018