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巴拿赫空间理论讲义 英文PDF|Epub|txt|kindle电子书版本网盘下载
- FernandoAlbiac，NigelJ.Kalton著 著
- 出版社： 北京：世界图书北京出版公司
- ISBN：9787510048043
- 出版时间：2012
- 标注页数：376页
- 文件大小：12MB
- 文件页数：388页
- 主题词：巴拿赫空间－教材－英文
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图书目录
1 Bases and Basic Sequences1
1.1 Schauder bases1
1.2 Examples:Fourier series6
1.3 Equivalence of bases and basic sequences10
1.4 Bases and basic sequences:discussion15
1.5 Constructing basic ？equences19
1.6 The Eberlein-？mulian Theorem23
Problems25
2 The Classical Sequence Spaces29
2.1 The isomorphic structure of the ep-spaces and c029
2.2 Complemented subspaces of ep（1≤p＜∞）and c033
2.3 The space e136
2.4 Convergence of series38
2.5 Complementability of c044
Problems48
3 Special Types of Bases51
3.1 Unconditional bases51
3.2 Boundedly-complete and shrinking bases53
3.3 Nonreflexive spaces with unconditional bases59
3.4 The James space ？62
3.5 A litmus test for unconditional bases66
Problems69
4 Banach Spaces of Continuous Functions73
4.1 Basic properties73
4.2 A characterization of real C(K)-spaces75
4.3 Isometrically injective spaces79
4.4 Spaces of continuous functions on uncountable compact metric spaces87
4.5 Spaces of continuous functions on countable compact metric spaces95
Problems98
5 L1（μ）-Spaces and C(K)-Spaces101
5.1 General remarks about L1（μ）-spaces101
5.2 Weakly compact subsets of L1（μ）103
5.3 Weak compactness in M(K)112
5.4 The Danford-Pettis property115
5.5 Weakly compact operators on C(K)-spaces118
5.6 Subspaces of L1（μ）-spaces and C(K)-spaces120
Problems122
6 The Lp-Spaces for 1≤p＜∞125
6.1 Conditional expectations and the Haar basis125
6.2 Averaging in Banach spaces131
6.3 Properties of L1142
6.4 Subspaces of Lp148
Problems161
7 Factorization Theory165
7.1 Maurey-Nikishin factorization theorems165
7.2 Subspaces of Lp for 1≤p＜2173
7.3 Factoring through Hilbert spaces180
7.4 The Kwapie？-Maurey theorems for type-2 spaces187
Problems191
8 Absolutely Summing Operators195
8.1 Grothendieck's Inequality196
8.2 Absolutely summing operators205
8.3 Absolutely summing operators on L1（μ）-spaces213
Problems217
9 Perfectly Homogeneous Bases and Their Applications221
9.1 Perfectly homogeneous bases221
9.2 Symmetric bases227
9.3 Uniqueness of unconditional basis229
9.4 Complementation of block basic sequences231
9.5 The existence of conditional bases235
9.6 Greedy bases240
Problems244
10 ep-Subspaces of Banach Spaces247
10.1 Ramsey theory247
10.2 Rosenthal's e1 theorem251
10.3 Tsirelson space254
Problems259
11 Finite Representability of ep-Spaces263
11.1 Finite representability263
11.2 The Principle of Local Reflexivity272
11.3 Krivine's theorem275
Problems285
12 An Introduction to Local Theory289
12.1 The John ellipsoid289
12.2 The concentration of measure phenomenon293
12.3 Dvoretzky's theorem296
12.4 The complemented subspace problem301
Problems306
13 Important Examples of Banach Spaces309
13.1 A generalization of the James space309
13.2 Constructing Banach spaces via trees314
13.3 Pelczy？ski's universal basis space316
13.4 The James tree space317
A Fundamental Notions327
B Elementary Hilbert Space Theory331
C Main Features of Finite-Dimensional Spaces335
D Cornerstone Theorems of Functional Analysis337
D.1 The Hahn-Banach Theorem337
D.2 Baire's Theorem and its consequences338
E Convex Sets and Extreme Points341
F The Weak Topologies343
G Weak Compactness of Sets and Operators347
List of Symbols349
References353
Index365