一些加强的算子平均不等式及YOUNG型不等式
发布时间：2018-12-08 11:39
【摘要】：在本文中,我们在给出几种算子平均的基础上并结合它们的性质得到了一些加强的包含正线性映射的算子平均不等式,进而研究了介于算术平均和几何平均之间的两个任意平均的算子不等式,最后,给出了关于矩阵的一些加强的Young型不等式.本文分为以下三个部分进行阐述.第一章,我们主要介绍几种算子平均的定义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和引理.第二章,我们运用第一章的基本定理及引理,对已有的一些重要算子不等式进行了强化.第三章,我们首先给出了加强的关于标量的Young型不等式.然后,基于这些不等式,建立了相应的算子不等式、关于Hilbert-Schmidt范数的矩阵不等式及行列式不等式.
[Abstract]:In this paper, on the basis of giving several operator averages and combining their properties, we obtain some strengthened operator averaging inequalities containing positive linear mappings. Then, two operator inequalities of arbitrary mean between arithmetic mean and geometric average are studied. Finally, some strengthened Young type inequalities for matrices are given. This article is divided into the following three parts to elaborate. In the first chapter, we mainly introduce the definition, properties and research background of the averaging of several operators, and give some basic theorems and lemmas involved in this paper. In the second chapter, we use the basic theorems and Lemma of the first chapter to strengthen some important operator inequalities. In chapter 3, we first give the Young type inequality about scalar quantity. Then, based on these inequalities, the corresponding operator inequalities, matrix inequalities and determinant inequalities for Hilbert-Schmidt norm are established.
【学位授予单位】：河南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O178;O177
本文编号：2368284
[Abstract]:In this paper, on the basis of giving several operator averages and combining their properties, we obtain some strengthened operator averaging inequalities containing positive linear mappings. Then, two operator inequalities of arbitrary mean between arithmetic mean and geometric average are studied. Finally, some strengthened Young type inequalities for matrices are given. This article is divided into the following three parts to elaborate. In the first chapter, we mainly introduce the definition, properties and research background of the averaging of several operators, and give some basic theorems and lemmas involved in this paper. In the second chapter, we use the basic theorems and Lemma of the first chapter to strengthen some important operator inequalities. In chapter 3, we first give the Young type inequality about scalar quantity. Then, based on these inequalities, the corresponding operator inequalities, matrix inequalities and determinant inequalities for Hilbert-Schmidt norm are established.
【学位授予单位】：河南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O178;O177
【参考文献】
相关期刊论文 前1条
1 胡兴凯;;矩阵的Young型不等式(英文)[J];华东师范大学学报(自然科学版);2012年04期
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