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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.

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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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1909年裏斯﹐F.(F.)給齣 [0﹐1]上連續綫性泛函的錶達式﹐這是分析學曆史上的重大事件。還有一個極重要的空間﹐那就是由所有在[0﹐1]上p次可勒貝格求和的函數構成的Lp空間(1<p<∞)。在1910～1917年﹐人們研究它的種種初等性質﹔其上連續綫性泛函的錶示﹐則照亮瞭通往對偶理論的道路。人們還把弗雷德霍姆積分方程理論推廣到這種空間﹐並且引進全連

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Banach空間

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巴拿赫空間

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許多在數學分析中學到的無限維函數空間都是巴拿赫空間，包括由連續函數（緊緻赫斯多夫空間上的連續函數）組成的空間、由勒貝格可積函數組成的L空間及由全純函數組成的哈代空間。上述空間是拓撲矢量空間中最常見的類型，這些空間的拓撲都自來其範數。

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值得擁有

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巴拿赫空間有兩種常見的類型：“實巴拿赫空間”及“復巴拿赫空間”，分彆是指將巴拿赫空間的矢量空間定義於由實數或復數組成的域之上。

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巴拿赫的主要貢獻是引進瞭綫性賦範空間概念，建立瞭其上的綫性算子理論，證明瞭作為泛函分析基礎的三個定理，哈恩--巴拿赫延拓定理，巴拿赫--斯坦豪斯定理即共鳴之定理、閉圖像定理。這些定理概括瞭許多經典的分析結果，在理論上和應用上都有重要價值。

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