Equality of three numerical radius inequalities

被引：4

作者：

Gau, Hwa-Long ^{[1
]}

Wu, Pei Yuan ^{[2
]}

机构：

[1] Natl Cent Univ, Dept Math, Chungli 32001, Taiwan

[2] Natl Chiao Tung Univ, Dept Appl Math, Hsinchu 30010, Taiwan

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2018年 / 554卷

关键词：

Numerical range; Numerical radius; Operator norm; Generalized Aluthge transform; P-HYPONORMAL OPERATORS;

D O I：

10.1016/j.laa.2018.05.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For an n-by-n matrix A, let w(A) and parallel to A parallel to denote its numerical radius and operator norm, respectively. The following three inequalities, each a strengthening of w(A) <= parallel to A parallel to, are known to hold: w(A)(2) <= (parallel to A parallel to(2) + w(A(2)))/2, w(A) <= (parallel to A parallel to + parallel to A(2)parallel to(1/2))/2, and w(A) <= (parallel to A parallel to + w(Delta(t)(A)))/2 (0 <= t <= 1), where Delta(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. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：51 / 67

页数：17

共 13 条

[1] A numerical radius inequality involving the generalized Aluthge transform [J].