巴拿赫空間講義（英文版） [Topics in Banach Space Theory] pdf epub mobi txt 電子書 下載 2025

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[美] 阿爾比亞剋（Fernando Albiac），Nigel J.Kalton 著

齣版社： 世界圖書齣版公司

ISBN：9787510048043

版次：1

商品編碼：11142969

包裝：平裝

外文名稱：Topics in Banach Space Theory

開本：24開

齣版時間：2012-09-01

用紙：膠版紙

頁數：188

正文語種：英文

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

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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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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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比當當亞馬遜都便宜10塊值瞭!!!!

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巴拿赫空間

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巴拿赫空間是以波蘭數學傢斯特凡·巴拿赫的名字來命名，他和漢斯·哈恩及愛德華·赫麗於1920-1922年提齣此空間。

評分☆☆☆☆☆

巴拿赫空間是一種賦有長度的綫性空間，大多數都是無窮空間，可看成通常嚮量空間的無窮維推廣。同時也是泛函分析研究的基本對象之一。

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巴拿赫空間

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紙張一般，發黃，而且還有爛瞭的

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無窮空間