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

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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 格式

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編輯本段

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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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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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Springer的GTM係列是研究生數學專著！專傢名著！推薦！

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巴拿赫空間

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不錯

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對偶空間

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巴拿赫空間

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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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