ESTIMATIONS OF HERON MEANS FOR POSITIVE OPERATORS

被引：7
|
作者：
Fujii, Masatoshi [1 ]
Furuichi, Shigeru [2 ]
Nakamoto, Ritsuo [3 ]
机构：
[1] Osaka Kyoiku Univ, Dept Math, Osaka 5828582, Japan
[2] Nihon Univ, Coll Humanities & Sci, Dept Informat Sci, Setagaya Ku, 3-25-40 Sakurajyousui, Tokyo 1568550, Japan
[3] Daihara Cho, Hitachi, Ibaraki 3160021, Japan
来源：
JOURNAL OF MATHEMATICAL INEQUALITIES | 2016年 / 10卷 / 01期
关键词：
Arithmetic mean; geometric mean; arithmetic-geometric mean inequality and Heron mean;
D O I：
10.7153/jmi-10-02
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The arithmetic-geometric mean inequality induces the path of Heron means through these two means by H-r(mu) (A,B) = r(A#B-mu)+(1-r)(A del B-mu) for each mu is an element of [0,1], r is an element of R and positive operators A, B on a Hilbert space. In this note, we estimate H-r(mu) (A, B) by the harmonic mean. As an application of this method, we refine the arithmetic-geometric mean inequality under the assumption of the strict order A-B >= m > 0.
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页码：19 / 30
页数：12
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