Springer數學經典教材：經典巴拿赫空間1和2 [Classical Banach Spaces 1 and 2] epub pdf mobi txt 電子書 下載 2024

Springer數學經典教材：經典巴拿赫空間1和2 [Classical Banach Spaces 1 and 2] epub pdf mobi txt 電子書 下載 2024

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Springer數學經典教材：經典巴拿赫空間1和2 [Classical Banach Spaces 1 and 2] epub pdf mobi txt 電子書 下載 2024

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內容簡介

《經典巴拿赫空間1和2》延續瞭該係列書的一貫風格，深入但不深沉。材料新穎，許多內容是同類書籍不具備的。對於學習Banach空間結構理論的學者來說，這是一本參考價值極高的書籍；對於學習該科目的讀者，《經典巴拿赫空間1和2》也是同等重要。目次：schauder 基；C0空間和lp空間；對稱基；O rlicz序列空間。
讀者對象：數學專業高年級的學生、老師和相關的科研人員。

內頁插圖

目錄

1. Schauder Bases
a. Existence of Bases and Examples
b. Schauder Bases and Duality
c. Unconditional Bases
d. Examples of Spaces Without an Unconditional Basis
e. The Approximation Property
f. Biorthogonal Systems
g. Schauder Decompositions

2. The Spaces co and lp
a. Projections in co and lp and Characterizations of these Spaces
b. Absolutely Summing Operators and Uniqueness of Unconditional Bases
c. Fredholm Operators， Strictly Singular Operators and Complemented Subspaces of lp lr
d. Subspaces of Co and lp and the Approximation Property， Complementably Universal Spaces
e. Banach Spaces Containing Iv or co
f. Extension and Lifting Properties， Automorphisms of loo， co and lx

3. Symmetric Bases
a. Properties of Symmetric Bases， Examples and Special Block Bases
b. Subspaces of Spaces with a Symmetric Basis

4. Orlicz Sequence Spaces
a. Subspaces of Orlicz Sequence Spaces which have a Symmetric Basis
b. Duality and Complemented Subspaces
c. Examples of Orlicz Sequence Spaces.
d. Modular Sequence Spaces and Subspaces of Ip lr
e. Lorentz Sequence Spaces
References
Subject Index

前言/序言

　　The appearance of Banachs book [8] in 1932 signified the beginning of a systematic study of normed linear spaces， which have been the subject of continuous research ever since.
　　In the sixties， and especially in the last decade， the research activity in this area
　　grew considerably. As a result， Banach space theory gained very much in depth as well as in scope. Most of its well known classical problems were solved， many interesting new directions were developed， and deep connections between Banach space theory and other areas of mathematics were established.
　　The purpose of this book is to present the main results and current research directions in the geometry of Banach spaces， with an emphasis on the study of the structure of the classical Banach spaces， that is C（K） and Lp（） and related spaces.We did not attempt to write a comprehensive survey of Banach space theory， or even only of the theory of classical Banach spaces， since the amount of interesting results on the subject makes such a survey practically impossible.
　　A part of the subject matter of this book appeared in outline in our lecture notes[96]. In contrast to those notes， most of the results presented here are given with complete proofs. We therefore hope that it will be possible to use the present book both as a text book on Banach space theory and as a reference book for research workers in the area. It contains much material which was not discussed in [96]， a large part of which being the result of very recent research work. An indication to the rapid recent progress in Banach space theory is the fact that most of the many problems stated in [96] have been solved by now.
　　In the present volume we also state some open problems. It is reasonable to expect that many of these will be solved in the not too far future. We feel， however，that most of the topics discussed here have reached a relatively final form， and that their presentation will not be radically affected by the solution of the open problems. Among the topics discussed in detail in this volume， the one which seems to us to be the least well understood and which might change the most in the future， is that of the approximation property.

Springer數學經典教材：經典巴拿赫空間1和2 [Classical Banach Spaces 1 and 2] epub pdf mobi txt 電子書 下載 2024

Springer數學經典教材：經典巴拿赫空間1和2 [Classical Banach Spaces 1 and 2] 下載 epub mobi pdf txt 電子書

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這本書覆蓋瞭從入門機械製圖工程師/技師所必需知道的關於産業的知識。書中還覆蓋瞭所必需的進階知識。 《實分析教程(第2版)(英文影印版)》是一部備受專傢好評的教科書，書中用現代的方式清晰論述瞭實分析的概念與理論，定理證明簡明易懂，可讀性強。在第一版的基礎上做瞭全麵修訂，有200道例題，練習題由原來的1200道增加到1300習題。本書的寫法像一部文學讀物，這在數學教科書很少見，因此閱讀本書會是一種享受。

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　　 目次：全書其有四部分，新增加瞭5章，總共17章。（一）集閤論、實數和微積分：集閤論；實數體係和微積分。（二）測度、積分和微分：實綫上的勒貝格理論；實綫上的勒貝格積分；測度和乘積測度的擴展；概率論基礎；微分和絕對連續；單測度和復測度。（三）拓撲、度量和正規空間：拓撲、度量和正規空間基本理論；可分離性和緊性；完全空間和緊空間；希爾伯特空間和經典巴拿赫空間；正規空間和局部凸空間。（四）調和分析、動力係統和hausdorff側都：調和分析基礎；可測動力係統；hausdorff測度和分形。

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