☆☆☆☆☆
简体网页||繁体网页



点击这里下载

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] 电子书 下载 mobi epub pdf txt

评分☆☆☆☆☆

Springer的GTM系列是研究生数学专著！专家名著！推荐！

评分☆☆☆☆☆

1909年里斯﹐F.(F.)给出 [0﹐1]上连续线性泛函的表达式﹐这是分析学历史上的重大事件。还有一个极重要的空间﹐那就是由所有在[0﹐1]上p次可勒贝格求和的函数构成的Lp空间(1<p<∞)。在1910～1917年﹐人们研究它的种种初等性质﹔其上连续线性泛函的表示﹐则照亮了通往对偶理论的道路。人们还把弗雷德霍姆积分方程理论推广到这种空间﹐并且引进全连

评分☆☆☆☆☆

里斯。F在1909年就给出了『0，1』上连续线性泛函的表达式。所以，连续线性泛函的表示是巴拿赫空间的一种初等性质。

评分☆☆☆☆☆

巴拿赫空间

评分☆☆☆☆☆

Springer的GTM系列是研究生数学专著！专家名著！推荐！

评分☆☆☆☆☆

巴拿赫空间

评分☆☆☆☆☆

好好好好好好

评分☆☆☆☆☆

巴拿赫的主要贡献是引进了线性赋范空间概念，建立了其上的线性算子理论，证明了作为泛函分析基础的三个定理，哈恩--巴拿赫延拓定理，巴拿赫--斯坦豪斯定理即共鸣之定理、闭图像定理。这些定理概括了许多经典的分析结果，在理论上和应用上都有重要价值。

评分☆☆☆☆☆

留着查资料用。很多东西不错的

类似图书 点击查看全场最低价