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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

目錄

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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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續算子的概念。當然還該想到希爾伯特空間。正是基於這些具體的﹑生動的素材﹐巴拿赫﹐S.與維納﹐N.相互獨立地在1922年提齣當今所謂巴拿赫空間的概念﹐並且在不到10年的時間內便發展成一部本身相當完美而又有著多方麵應用的理論。

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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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留著查資料用。很多東西不錯的

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到?上的綫性函數。若?(x)還是連續的，則稱?(x)為連續綫性泛函。一切如此的?(x)按範數構成的巴拿赫空間，便稱為X的對偶空間(或共軛空間)並記作X*（或X┡）。　在許多數學分支中都會遇到對偶空間，例如矩量問題、偏微分方程理論等。一些物理係統的狀態也常與適當空間上的綫性泛函聯係在一起。至於泛函分析本身，對偶空間也是極為重要的概念。通過X*,能更好地理解X。

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對偶空間

評分☆☆☆☆☆

留著查資料用。很多東西不錯的

評分☆☆☆☆☆

留著查資料用。很多東西不錯的

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Banach空間

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