本文選題：Cesaro序列空間 + 緊強(qiáng)凸點(diǎn)　； 參考：《哈爾濱理工大學(xué)》2015年碩士論文

【摘要】：Banach空間理論是泛函分析的一個重要的研究方向，也是現(xiàn)今數(shù)學(xué)極具理論意義和應(yīng)用價值的研究課題。Banach空間理論的建立和發(fā)展，不僅延伸了泛函分析學(xué)科的內(nèi)容，，而且也為其他領(lǐng)域的科學(xué)和技術(shù)帶來了更為普遍的應(yīng)用。Banach空間的幾何性質(zhì)是Banach空間理論中的重要研究內(nèi)容之一。本文主要研究兩類具體的Banach序列空間—Cesaro序列空間和Musielak-Orlicz序列空間的一些幾何性質(zhì)和點(diǎn)態(tài)性質(zhì)。全文共分三個部分，主要工作總結(jié)如下： 第一章是緒論。在這一章中，我們首先介紹了課題研究的目的和意義，然后詳細(xì)闡述了Banach空間幾何理論的國內(nèi)外研究發(fā)展?fàn)顩r，最后展示了本文各部分所討論的主要內(nèi)容。 在第二章中，我們首先將Banach空間中的強(qiáng)凸性質(zhì)和緊強(qiáng)凸性質(zhì)的概念進(jìn)行了推廣，引入了強(qiáng)凸點(diǎn)和緊強(qiáng)凸點(diǎn)的定義。然后給出了Banach空間中強(qiáng)凸點(diǎn)與緊強(qiáng)凸點(diǎn)之間的關(guān)系。最后在一類具體的Banach空間—Cesaro序列空間cesp中我們討論了緊強(qiáng)凸性質(zhì)的刻畫問題。同時證明了Cesaro序列空間cesp當(dāng)1＜p＜∞時，具有(K)性質(zhì)和弱正交性質(zhì)。 在第三章中，我們給出了局部β性質(zhì)在賦Orlicz范數(shù)的Musielak-Orlicz序列空間中的等價條件。首先討論了賦Orlicz范數(shù)的Musielak-Orlicz序列空間中的β點(diǎn)的具體刻畫問題，然后利用已得到的β點(diǎn)的判據(jù)得出了賦Orlicz范數(shù)的Musielak-Orlicz序列空間具有局部β性質(zhì)的充要條件。
[Abstract]:Banach space theory is an important research direction of functional analysis, and it is also the establishment and development of Banach space theory, which is of great theoretical significance and application value in mathematics nowadays, which not only extends the content of functional analysis.It is also one of the important research contents in Banach space theory that it brings more general applications to other fields of science and technology.In this paper, we mainly study some geometric properties and pointwise properties of two classes of Banach sequence space, Cesaro sequence space and Musielak-Orlicz sequence space.The paper is divided into three parts. The main work is summarized as follows:The first chapter is the introduction.In this chapter, we first introduce the purpose and significance of the research, then elaborate the research and development of Banach space geometry theory at home and abroad, and finally show the main contents discussed in each part of this paper.In chapter 2, we first generalize the concepts of strong convex property and compact strong convex property in Banach space, and introduce the definitions of strong convex point and compact strong convex point.Then the relation between the strong convex point and the compact strong convex point in Banach space is given.Finally, we discuss the characterization of compact strong convexity in a class of Banach space Cesaro sequence space cesp.At the same time, it is proved that the Cesaro sequence space cesp has the property of K) and the property of weak orthogonality when 1 < p < 鈭

本文編號：1753905