A New Majorization Induced by Matrix Order

被引：0

作者：

Uchiyama, Mitsuru ^{[1
]}

机构：

[1] Shimane Univ, Interdisciplinary Fac Sci & Engn, Dept Math, Matsue, Shimane 6908504, Japan

来源：

RECENT ADVANCES IN OPERATOR THEORY AND APPLICATIONS | 2009年 / 187卷

关键词：

Matrix order; operator inequality; operator monotone function; majorization; OPERATOR; INEQUALITIES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let h be a non-decreasing function on I and k air increasing function on J. Then h, is said to be majorized by k, in symbols h <= k if J subset of I and h o k(-1) is operator monotone on k(J), that is if sigma(A), sigma(B) subset of J, k(A) <= k(B) double right arrow h(A) <= h(B). We will give a condition for h in order that h' <= h.

引用

页码：211 / 216

页数：6

共 10 条

[1] ON SOME OPERATOR INEQUALITIES [J].

ANDO, T .

MATHEMATISCHE ANNALEN, 1987, 279 (01) :157-159

[2] A matrix subadditivity inequality for f (A+B) and f(A)+f(B) [J].

Bourin, Jean-Christophe ;

Uchiyama, Mitsuru .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 423 (2-3) :512-518

[3] FURUTA INEQUALITY AND ITS APPLICATION TO ANDO THEOREM [J].

FUJII, M ;

FURUTA, T ;

KAMEI, E .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1993, 179 :161-169

[4]

FURUTA T, 1987, P AM MATH SOC, V101, P85

[5] Inequalities between ∥f(A+B)∥ and ∥f(A)+f(B)∥ [J].

Kosem, Tomaz .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 418 (01) :153-160

[6] Operator monotone functions which are defined implicitly and operator inequalities [J].

Uchiyama, M .

JOURNAL OF FUNCTIONAL ANALYSIS, 2000, 175 (02) :330-347

[7] A new majorization between functions, polynomials, and operator inequalities [J].

Uchiyama, M .

JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 231 (01) :221-244

[8]

Uchiyama M, 1999, MATH INEQUAL APPL, V2, P469

[9] On some operator monotone functions [J].

Uchiyama, M ;

Hasumi, M .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2002, 42 (02) :243-251

[10] A new majorization between functions, polynomials, and operator inequalities II [J].

Uchiyama, Mitsuru .

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2008, 60 (01) :291-310

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