一些數值半徑不等式其等式情形之研究;A Study on Equality Case of Some Numerical Radius Inequalities

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/78794

Title:	一些數值半徑不等式其等式情形之研究;A Study on Equality Case of Some Numerical Radius Inequalities
Authors:	高華隆
Contributors:	國立中央大學數學系
Keywords:	Aluthge轉換;數值半徑;Aluthge transform;numerical radius
Date:	2018-12-19
Issue Date:	2018-12-20 13:49:26 (UTC+8)
Publisher:	科技部
Abstract:	令A=U\|A\| 為一n乘n矩陣A的極分解。而D_t(A)=\|A\|^t U\|A\|^(1-t)對於t屬於[0,1], 稱之為A的廣義Aluthge轉換。本計畫的目的在於研究A的廣義Aluthge轉換的數值半徑其行為，特別的，對於以下的數值半徑不等式:(1) 2w(A) - ‖A‖ ≦ w(D_t(A)) ≦ w(A),(2) w(A) ≦ (‖A‖ + ‖A^2‖^(1/2))/2, and(3) w(A)^2 ≦ (‖A‖^2 + w(A^2))/2.我們將考慮這些不等式何時等式成立。對於每一個不等式，我們將給出等式成立的充分必要條件。 ;Let A=U\|A\| be the polar decomposition of an n-by-n matrix A. The generalized Aluthge transform is then given by D_t(A)=\|A\|^t U\|A\|^(1-t) for t in [0,1]. We investigate the behavior of the numerical radius w(D_t(A)). In particular, for the following numerical radius inequalities:(1) 2w(A) - ∥A∥ ≦ w(D_t(A)) ≦ w(A),(2) w(A) ≦ (∥A∥ + ∥A^2∥^(1/2))/2, and(3) w(A)^2 ≦ (∥A∥^2 + w(A^2))/2.We consider when these inequalities become equalities. We want to give complete characterizations of A for which the equality is attained.
Relation:	財團法人國家實驗研究院科技政策研究與資訊中心
Appears in Collections:	[Department of Mathematics] Research Project

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