Jensen's operator inequality for functions of several variables

被引：24

作者：

Araki, H ^{[1
]}

Hansen, F

机构：

[1] Sci Univ Tokyo, Fac Sci & Technol, Dept Math, Noda, Chiba 2788510, Japan

[2] Univ Copenhagen, Inst Econ, DK-1455 Copenhagen K, Denmark

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2000年 / 128卷 / 07期

关键词：

D O I：

10.1090/S0002-9939-00-05371-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The operator convex functions of several variables are characterized in terms of a non-commutative generalization of Jensen's inequality, extending previous results of F. Hansen and G.K. Pedersen for functions of one variable and of F. Hansen for functions of two variables.

引用

页码：2075 / 2084

页数：10

共 9 条

[1] CONCAVITY OF CERTAIN MAPS ON POSITIVE DEFINITE MATRICES AND APPLICATIONS TO HADAMARD PRODUCTS [J].

ANDO, T .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1979, 26 (AUG) :203-241

[2] MATRIX CONVEXITY OF FUNCTIONS OF 2 VARIABLES [J].

AUJLA, JS .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1993, 194 :149-160

[3]

Halmos, 2012, HILBERT SPACE PROBLE, V19

[4] Operator convex functions of several variables [J].

Hansen, F .

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 1997, 33 (03) :443-463

[5] Jensen's operator inequality for functions of two variables [J].

Hansen, F .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 125 (07) :2093-2102

[6] OPERATOR-INEQUALITY [J].

HANSEN, F .

MATHEMATISCHE ANNALEN, 1980, 246 (03) :249-250

[7] JENSEN INEQUALITY FOR OPERATORS AND LOWNER THEOREM [J].

HANSEN, F ;

PEDERSEN, GK .

MATHEMATISCHE ANNALEN, 1982, 258 (03) :229-241

[8]

Koranyi A., 1961, Trans. Am. Math. Soc, V101, P520, DOI [10.2307/1993476, 10.1090/S0002-9947-1961-0136765-6, DOI 10.1090/S0002-9947-1961-0136765-6]

[9] EXTREME N-TUPLES OF ELEMENTS IN C-STAR-ALGEBRAS [J].

PEDERSEN, GK .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1987, 19 :264-270

← 1 →