Banach序列空间的若干几何性质

发布时间：2018-04-15 11:20

  本文选题：Cesaro序列空间 + 紧强凸点　； 参考：《哈尔滨理工大学》2015年硕士论文

【摘要】：Banach空间理论是泛函分析的一个重要的研究方向，也是现今数学极具理论意义和应用价值的研究课题。Banach空间理论的建立和发展，不仅延伸了泛函分析学科的内容，，而且也为其他领域的科学和技术带来了更为普遍的应用。Banach空间的几何性质是Banach空间理论中的重要研究内容之一。本文主要研究两类具体的Banach序列空间—Cesaro序列空间和Musielak-Orlicz序列空间的一些几何性质和点态性质。全文共分三个部分，主要工作总结如下： 第一章是绪论。在这一章中，我们首先介绍了课题研究的目的和意义，然后详细阐述了Banach空间几何理论的国内外研究发展状况，最后展示了本文各部分所讨论的主要内容。 在第二章中，我们首先将Banach空间中的强凸性质和紧强凸性质的概念进行了推广，引入了强凸点和紧强凸点的定义。然后给出了Banach空间中强凸点与紧强凸点之间的关系。最后在一类具体的Banach空间—Cesaro序列空间cesp中我们讨论了紧强凸性质的刻画问题。同时证明了Cesaro序列空间cesp当1＜p＜∞时，具有(K)性质和弱正交性质。 在第三章中，我们给出了局部β性质在赋Orlicz范数的Musielak-Orlicz序列空间中的等价条件。首先讨论了赋Orlicz范数的Musielak-Orlicz序列空间中的β点的具体刻画问题，然后利用已得到的β点的判据得出了赋Orlicz范数的Musielak-Orlicz序列空间具有局部β性质的充要条件。
[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

本文编号：1753905