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內容簡介

　　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.

內頁插圖

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前言/序言

巴拿赫空間講義（英文版） [Topics in Banach Space Theory] 下載 mobi epub pdf txt 電子書

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不錯

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不錯

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設 ?(x)是從實(或復)數域上賦範綫性空間X

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巴拿赫空間

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裏斯。F在1909年就給齣瞭『0，1』上連續綫性泛函的錶達式。所以，連續綫性泛函的錶示是巴拿赫空間的一種初等性質。

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值得擁有

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巴拿赫空間（Banach space）是一種賦有“長度”的綫性空間﹐泛函分析研究的基本對象之一。數學分析各個分支的發展為巴拿赫空間理論的誕生提供瞭許多豐富而生動的素材。從外爾斯特拉斯﹐K.(T.W.)以來﹐人們久已十分關心閉區間[a﹐b ]上的連續函數以及它們的一緻收斂性。甚至在19世紀末﹐G.阿斯科利就得到[a﹐b ]上一族連續函數之列緊性的判斷準則﹐後來十分成功地用於常微分方程和復變函數論中。

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完備的綫性賦範空間稱為巴拿赫空間。是用波蘭數學傢巴拿赫(Stefan Banach ）的名字命名的。

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在數學裏，尤其是在泛函分析之中，巴拿赫空間是一個完備賦範矢量空間。更精確地說，巴拿赫空間是一個具有範數並對此範數完備的矢量空間。

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