【摘要】：Banach空間幾何理論是泛函分析的重要研究內(nèi)容,其中幾何常數(shù)是研究幾何結(jié)構(gòu)和不動點性質(zhì)的一個重要工具。本文主要對Banach空間和Orlicz空間的一些幾何常數(shù)進行了研究,得出此類幾何常數(shù)的計算公式以及與其它幾何性質(zhì)與空間性質(zhì)的關(guān)系。全文共分四章,主要研究如下:第一章主要介紹了 Banach空間和Orlicz空間理論的發(fā)展歷史和背景,闡述研究Banach空間和Orlicz空間幾何性質(zhì)的意義,并給出本文研究的主要內(nèi)容。第二章Banach空間X中引入了一個新的幾何常數(shù)C_2~(p)(X),稱為廣義的Zbaganu常數(shù)。計算了該常數(shù)在Banach空間X中的上下界估計值,給出了 X是一致非方的等價條件,并討論了C_z~(p)(X)常數(shù)與James常數(shù)之間的關(guān)系,將C_z~(p)(X)常數(shù)與不動點性質(zhì)建立聯(lián)系。第三章在本章證明ΓX(t)=t時,Kothe序列空間沒有絕對連續(xù)范數(shù)。此外,在賦Luxemburg范數(shù)的Orlicz空間中給出接近一致光滑模的公式,并且根據(jù)定義與已知條件找出賦Luxemburg范數(shù)的Or1icz空間是接近一致光滑的條件。而且根據(jù)以上得出的結(jié)論,證明出R(a,l_(Φ)1+a和RW(a,l_(Φ)1+α的等價條件。第四章在本章中討論在賦Orlicz范數(shù)的Orlicz空間中的一些接近一致光滑模的新結(jié)果,并且給出其在不動點性質(zhì)中的應(yīng)用。同時給出了這個模的一些重要公式,并舉出具體空間中的例子說明其重要性。
[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 偽. 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.
【學(xué)位授予單位】：哈爾濱理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O177

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本文編號：2209223