巴拿赫空间讲义（英文版） [Topics in Banach Space Theory] epub pdf mobi txt 电子书 下载 2024

巴拿赫空间讲义（英文版） [Topics in Banach Space Theory] epub pdf mobi txt 电子书 下载 2024

☆☆☆☆☆
简体网页||繁体网页



点击这里下载

巴拿赫空间讲义（英文版） [Topics in Banach Space Theory] epub pdf mobi txt 电子书 下载 2024

类似图书 点击查看全场最低价

---

内容简介

　　This book grew out of a one-semester course given by the second author in 2001 and a subsequent two-semester course in 2004-2005， both at the University of Missouri-Columbia. The text is intended for a graduate student who has already had a basic introduction to functional analysis; the'aim is to give a reasonably brief and self-contained introduction to classical Banach space theory.
　　Banach space theory has advanced dramatically in the last 50 years and we believe that the techniques that have been developed are very powerful and should be widely disseminated amongst analysts in general and not restricted to a small group of specialists. Therefore we hope that this book will also prove of interest to an audience who may not wish to pursue research in this area but still would like to understand what is known about the structure of the classical spaces.
　　Classical Banach space theory developed as an attempt to answer very natural questions on the structure of Banach spaces; many of these questions date back to the work of Banach and his school in Lvov. It enjoyed， perhaps， its golden period between 1950 and 1980， culminating in the definitive books by Lindenstrauss and Tzafriri [138] and [139]， in 1977 and 1979 respectively. The subject is still very much alive but the reader will see that much of the basic groundwork was done in this period.
　　At the same time， our aim is to introduce the student to the fundamental techniques available to a Banach space theorist. As an example， we spend much of the early chapters discussing the use of Schauder bases and basic sequences in the theory. The simple idea of extracting basic sequences in order to understand subspace structure has become second-nature in the subject， and so the importance of this notion is too easily overlooked.
　　It should be pointed out that this book is intended as a text for graduate students， not as a reference work， and we have selected material with an eye to what we feel can be appreciated relatively easily in a quite leisurely two-semester course. Two of the most spectacular discoveries in this area during the last 50 years are Enfio's solution of the basis problem [54] and the Gowers-Maurey solution of the unconditional basic sequence problem [71]. The reader will find discussion of these results but no presentation. Our feeling， based on experience， is that detouring from the development of the theory to present lengthy and complicated counterexamples tends to break up the flow of the course. We prefer therefore to present only relatively simple and easily appreciated counterexamples such as the James space and Tsirelson's space. We also decided， to avoid disruption， that some counterexamples of intermediate difficulty should be presented only in the last optional chapter and not in the main body of the text.

内页插图

目录

;



;

前言/序言

巴拿赫空间讲义（英文版） [Topics in Banach Space Theory] epub pdf mobi txt 电子书 下载 2024

巴拿赫空间讲义（英文版） [Topics in Banach Space Theory] 下载 epub mobi pdf txt 电子书 2024

评分☆☆☆☆☆

巴拿赫空间有两种常见的类型：“实巴拿赫空间”及“复巴拿赫空间”，分别是指将巴拿赫空间的矢量空间定义于由实数或复数组成的域之上。

评分☆☆☆☆☆

巴拿赫空间（Banach space）是一种赋有“长度”的线性空间﹐泛函分析研究的基本对象之一。数学分析各个分支的发展为巴拿赫空间理论的诞生提供了许多丰富而生动的素材。从外尔斯特拉斯﹐K.(T.W.)以来﹐人们久已十分关心闭区间[a﹐b ]上的连续函数以及它们的一致收敛性。甚至在19世纪末﹐G.阿斯科利就得到[a﹐b ]上一族连续函数之列紧性的判断准则﹐后来十分成功地用于常微分方程和复变函数论中。

评分☆☆☆☆☆

完备的线性赋范空间称为巴拿赫空间。是用波兰数学家巴拿赫(Stefan Banach ）的名字命名的。

评分☆☆☆☆☆

设 ?(x)是从实(或复)数域上赋范线性空间X

评分☆☆☆☆☆

好好好好好好

评分☆☆☆☆☆

许多在数学分析中学到的无限维函数空间都是巴拿赫空间，包括由连续函数（紧致赫斯多夫空间上的连续函数）组成的空间、由勒贝格可积函数组成的L空间及由全纯函数组成的哈代空间。上述空间是拓扑矢量空间中最常见的类型，这些空间的拓扑都自来其范数。

评分☆☆☆☆☆

许多在数学分析中学到的无限维函数空间都是巴拿赫空间，包括由连续函数（紧致赫斯多夫空间上的连续函数）组成的空间、由勒贝格可积函数组成的L空间及由全纯函数组成的哈代空间。上述空间是拓扑矢量空间中最常见的类型，这些空间的拓扑都自来其范数。

评分☆☆☆☆☆

巴拿赫空间有两种常见的类型：“实巴拿赫空间”及“复巴拿赫空间”，分别是指将巴拿赫空间的矢量空间定义于由实数或复数组成的域之上。

评分☆☆☆☆☆

比当当亚马逊都便宜10块值了!!!!

类似图书 点击查看全场最低价