算子不等式与加权几何平均的回旋线

IF 0.9 4区数学 Q2 MATHEMATICS

Mathematical Inequalities & Applications Pub Date : 2020-09-22 DOI:10.7153/MIA-2021-24-34

Sejong Kim

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引用次数: 11

摘要

本文考虑了正定算子的两种不同类型的加权几何均值。我们给出了这些几何均值的分量双射，并给出了作为度量中点的谱几何均值的几何性质。此外，还将给出与正定算子的几何均值有关的几个有趣的不等式。在有限维旋群结构中，我们也看到了加权几何平均的意义，并得到了2乘2正定矩阵和密度矩阵的加权几何平均公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Operator inequalities and gyrolines of the weighted geometric means

We consider in this paper two different types of the weighted geometric means of positive definite operators. We show the component-wise bijection of these geometric means and give a geometric property of the spectral geometric mean as a metric midpoint. Moreover, several interesting inequalities related with the geometric means of positive definite operators will be shown. We also see the meaning of weighted geometric means in the gyrogroup structure with finite dimension and find the formulas of weighted geometric means of 2-by-2 positive definite matrices and density matrices.

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来源期刊

Mathematical Inequalities & Applications 数学-数学

CiteScore

2.30

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： ''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.