Orlicz空间的接近光滑模
发布时间：2018-08-28 11:11
【摘要】：Banach空间几何理论是泛函分析的重要研究内容,其中几何常数是研究几何结构和不动点性质的一个重要工具。本文主要对Banach空间和Orlicz空间的一些几何常数进行了研究,得出此类几何常数的计算公式以及与其它几何性质与空间性质的关系。全文共分四章,主要研究如下:第一章主要介绍了 Banach空间和Orlicz空间理论的发展历史和背景,阐述研究Banach空间和Orlicz空间几何性质的意义,并给出本文研究的主要内容。第二章Banach空间X中引入了一个新的几何常数C_2~(p)(X),称为广义的Zbaganu常数。计算了该常数在Banach空间X中的上下界估计值,给出了 X是一致非方的等价条件,并讨论了C_z~(p)(X)常数与James常数之间的关系,将C_z~(p)(X)常数与不动点性质建立联系。第三章在本章证明ΓX(t)=t时,Kothe序列空间没有绝对连续范数。此外,在赋Luxemburg范数的Orlicz空间中给出接近一致光滑模的公式,并且根据定义与已知条件找出赋Luxemburg范数的Or1icz空间是接近一致光滑的条件。而且根据以上得出的结论,证明出R(a,l_(Φ)1+a和RW(a,l_(Φ)1+α的等价条件。第四章在本章中讨论在赋Orlicz范数的Orlicz空间中的一些接近一致光滑模的新结果,并且给出其在不动点性质中的应用。同时给出了这个模的一些重要公式,并举出具体空间中的例子说明其重要性。
[Abstract]:Banach space geometry theory is an important research content in functional analysis, in which geometric constants are an important tool for studying geometric structure and fixed point properties. In this paper, some geometric constants of Banach space and Orlicz space are studied, and the formulas for calculating these geometric constants are obtained, as well as their relations with other geometric properties and space properties. The thesis is divided into four chapters. The first chapter mainly introduces the history and background of Banach space and Orlicz space theory, expounds the significance of studying the geometric properties of Banach space and Orlicz space, and gives the main contents of this paper. In chapter 2, we introduce a new geometric constant C _ 2 ~ (p) (X), called generalized Zbaganu constant in Banach space X. In this paper, the upper and lower bounds of the constant in Banach space X are calculated, and the equivalent conditions for X to be uniformly nonsquare are given. The relation between the James constant and the (p) (X) constant is discussed, and the relation between the (p) (X) constant and the fixed point property is established. In chapter 3, we prove that 螕 X (t) t has no absolute continuous norm in sequence space. In addition, in the Orlicz space with Luxemburg norm, we give the formula of nearly uniformly smooth module, and find out the condition that the Or1icz space with Luxemburg norm is nearly uniformly smooth according to the definition and known conditions. Based on the above conclusions, we prove the equivalent conditions for R (ahl桅) 1a and RW (ahl桅) 1 伪. In chapter 4, in this chapter, we discuss some new results of nearly uniformly smooth modules in Orlicz spaces with Orlicz norm, and give their applications in fixed point properties. At the same time, some important formulas of this module are given, and an example in the concrete space is given to illustrate its importance.
【学位授予单位】：哈尔滨理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177
本文编号：2209223
[Abstract]:Banach space geometry theory is an important research content in functional analysis, in which geometric constants are an important tool for studying geometric structure and fixed point properties. In this paper, some geometric constants of Banach space and Orlicz space are studied, and the formulas for calculating these geometric constants are obtained, as well as their relations with other geometric properties and space properties. The thesis is divided into four chapters. The first chapter mainly introduces the history and background of Banach space and Orlicz space theory, expounds the significance of studying the geometric properties of Banach space and Orlicz space, and gives the main contents of this paper. In chapter 2, we introduce a new geometric constant C _ 2 ~ (p) (X), called generalized Zbaganu constant in Banach space X. In this paper, the upper and lower bounds of the constant in Banach space X are calculated, and the equivalent conditions for X to be uniformly nonsquare are given. The relation between the James constant and the (p) (X) constant is discussed, and the relation between the (p) (X) constant and the fixed point property is established. In chapter 3, we prove that 螕 X (t) t has no absolute continuous norm in sequence space. In addition, in the Orlicz space with Luxemburg norm, we give the formula of nearly uniformly smooth module, and find out the condition that the Or1icz space with Luxemburg norm is nearly uniformly smooth according to the definition and known conditions. Based on the above conclusions, we prove the equivalent conditions for R (ahl桅) 1a and RW (ahl桅) 1 伪. In chapter 4, in this chapter, we discuss some new results of nearly uniformly smooth modules in Orlicz spaces with Orlicz norm, and give their applications in fixed point properties. At the same time, some important formulas of this module are given, and an example in the concrete space is given to illustrate its importance.
【学位授予单位】：哈尔滨理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177
【参考文献】
相关期刊论文 前3条
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3 王廷辅,陈述涛;Orlicz空间的光滑性[J];工程数学学报;1987年03期
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