【摘要】：在本文中,我們在給出幾種算子平均的基礎(chǔ)上并結(jié)合它們的性質(zhì)得到了一些加強(qiáng)的包含正線性映射的算子平均不等式,進(jìn)而研究了介于算術(shù)平均和幾何平均之間的兩個(gè)任意平均的算子不等式,最后,給出了關(guān)于矩陣的一些加強(qiáng)的Young型不等式.本文分為以下三個(gè)部分進(jìn)行闡述.第一章,我們主要介紹幾種算子平均的定義和性質(zhì)以及研究背景,并給出了本文中涉及到的一些基本定理和引理.第二章,我們運(yùn)用第一章的基本定理及引理,對已有的一些重要算子不等式進(jìn)行了強(qiáng)化.第三章,我們首先給出了加強(qiáng)的關(guān)于標(biāo)量的Young型不等式.然后,基于這些不等式,建立了相應(yīng)的算子不等式、關(guān)于Hilbert-Schmidt范數(shù)的矩陣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.
【學(xué)位授予單位】：河南師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O178;O177

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 胡興凱;;矩陣的Young型不等式(英文)[J];華東師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2012年04期

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本文編號：2368284