巴拿赫空间讲义（英文版） [Topics in Banach Space Theory] 下载 mobi epub pdf 电子书 2025

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

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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。

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对偶空间

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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。

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巴拿赫空间

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巴拿赫空间

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