若干算子平均和矩阵平均的不等式的研究

发布时间：2018-12-14 07:27

【摘要】：本文在Heinz平均与几何平均的基础上,通过结合它们的性质得到了一些包含正线性映射的算子不等式和矩阵范数不等式以及矩阵奇异值不等式.本文分为以下两个部分进行阐述.第一章,主要介绍几何平均与Heinz平均的概念和性质以及研究背景,并给出了本文中涉及到的一些基本定理.第二章,在Diaz-Metcalf型算子不等式的基础上,利用几何平均和Heinz平均的性质得到了一些包含正线性映射的几何平均和Heinz平均的算子不等式.并且以包含正线性映射的加权几何平均在p(p ≥ 2)次幂下保序的不等式为基础,对Heinz平均的算子不等式做了进一步的推广.此外,由矩阵的范数不等式,K对称张量积的性质定理以及K对称张量积与奇异值的关系,得到了一些矩阵不等式.
[Abstract]:In this paper, on the basis of Heinz mean and geometric average, some operator inequalities, matrix norm inequalities and matrix singular value inequalities containing positive linear mappings are obtained by combining their properties. This article is divided into the following two parts to elaborate. In the first chapter, the concepts and properties of geometric average and Heinz average are introduced, and some basic theorems are given. In chapter 2, on the basis of Diaz-Metcalf type operator inequality, we obtain some operator inequalities containing geometric mean and Heinz average of positive linear mappings by using the properties of geometric mean and Heinz average. Furthermore, based on the order preserving inequality of weighted geometric mean with positive linear mapping under p (p 鈮，

本文编号：2378189