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　　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.

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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

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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。

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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。

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设 ?(x)是从实(或复)数域上赋范线性空间X

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纸张一般，发黄，而且还有烂了的

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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

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设 ?(x)是从实(或复)数域上赋范线性空间X

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到?上的线性函数。若?(x)还是连续的，则称?(x)为连续线性泛函。一切如此的?(x)按范数构成的巴拿赫空间，便称为X的对偶空间(或共轭空间)并记作X*（或X┡）。　在许多数学分支中都会遇到对偶空间，例如矩量问题、偏微分方程理论等。一些物理系统的状态也常与适当空间上的线性泛函联系在一起。至于泛函分析本身，对偶空间也是极为重要的概念。通过X*,能更好地理解X。

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☆☆☆☆☆

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

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