Cartesian decomposition and numerical radius inequalities

被引：76

作者：

Kittaneh, Fuad ^{[1
]}

Moslehian, Mohammad Sal ^{[2
]}

Yamazaki, Takeaki ^{[3
]}

机构：

[1] Univ Jordan, Dept Math, Amman, Jordan

[2] Ferdowsi Univ Mashhad, Dept Pure Math, Ctr Excellence Anal Algebra Struct, Mashhad 91775, Iran

[3] Toyo Univ, Dept Elect Elect & Comp Engn, Kawagoe, Saitama 8508585, Japan

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2015年 / 471卷

关键词：

Numerical radius; Positive operator; Cartesian decomposition; Triangle inequality; HILBERT-SPACE OPERATORS; EQUALITY; NORM;

D O I：

10.1016/j.laa.2014.12.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that if T = H + iK is the Cartesian decomposition of T is an element of B(H), then for alpha, beta is an element of R, sup(alpha 2+beta 2=1) parallel to alpha H + beta K parallel to = w(T). We then apply it to prove that if A, B, X is an element of B(H) and 0 <= mI <= X, then m parallel to Re(A) - Re(B)parallel to <= w (Re(A)X - XRe(B)) <= 1/2sup (theta is an element of R)parallel to(AX - XB) + e(i theta) (XA - BX)parallel to <=parallel to AX - XB parallel to + parallel to XA - BX parallel to/2, where Re(T) denotes the real part of an operator T. A refinement of the triangle inequality is also shown. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：46 / 53

页数：8

共 13 条

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