發(fā)布時間：2018-12-14 07:27

【摘要】：本文在Heinz平均與幾何平均的基礎(chǔ)上,通過結(jié)合它們的性質(zhì)得到了一些包含正線性映射的算子不等式和矩陣范數(shù)不等式以及矩陣奇異值不等式.本文分為以下兩個部分進(jìn)行闡述.第一章,主要介紹幾何平均與Heinz平均的概念和性質(zhì)以及研究背景,并給出了本文中涉及到的一些基本定理.第二章,在Diaz-Metcalf型算子不等式的基礎(chǔ)上,利用幾何平均和Heinz平均的性質(zhì)得到了一些包含正線性映射的幾何平均和Heinz平均的算子不等式.并且以包含正線性映射的加權(quán)幾何平均在p(p ≥ 2)次冪下保序的不等式為基礎(chǔ),對Heinz平均的算子不等式做了進(jìn)一步的推廣.此外,由矩陣的范數(shù)不等式,K對稱張量積的性質(zhì)定理以及K對稱張量積與奇異值的關(guān)系,得到了一些矩陣不等式.
[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，

本文編號：2378189