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GTM96泛函分析教程 第2版PDF|Epub|txt|kindle电子书版本网盘下载
- J.B.Conway编 著
- 出版社： 北京：世界图书出版公司
- ISBN：7506259516
- 出版时间：2003
- 标注页数：399页
- 文件大小：126MB
- 文件页数：419页
- 主题词：泛函分析－研究生－教材－英文
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图书目录
CHAPTER Ⅰ Hilbert Spaces1
1．Elementary Properties and Examples1
2．Orthogonality7
3．The Riesz Representation Theorem11
4．Orthonormal Sets of Vectors and Bases14
5．Isomorphic Hilbert Spaces and the Fourier Transform for the Circle19
6．The Direct Sum of Hilbert Spaces23
CHAPTER Ⅱ Operators on Hilbert Space26
1．Elementary Properties and Examples26
2．The Adioint of an Operator31
3．Projections and Idempotents;Invariant and Reducing Subspaces36
4．Compact Operators41
5．The Diagonalization of Compact Self-Adjoint Operators46
6．An Application:Sturm-Liouville Systems49
7．The Spectral Theorem and Functional Calculus for Compact Normal Operators54
8．Unitary Equivalence for Compact Normal Operators60
CHAPTER Ⅲ Banach Spaces63
1．Elementary Properties and Examples63
2．Linear Operators on Normed Spaces67
3．Finite Dimensional Normed Spaces69
4．Quotients and Products of Normed Spaces70
5．Linear Functionals73
6．The Hahn-Banach Theorem77
7．An Application:Banach Limits82
8．An Application:Runge's Theorem83
9．An Application:Ordered Vector Spaces86
10．The Dual of a Quotient Space and a Subspace88
11．Reflexive Spaces89
12．The Open Mapping and Closed Graph Theorems90
13．Complemented Subspaces of a Banach Space93
14．The Principle of Uniform Boundedness95
CHAPTER Ⅳ Locally Convex Spaces99
1．Elementary Properties and Examples99
2．Metrizable and Normable Locally Convex Spaces105
3．Some Geometric Consequences of the Hahn-Banach Theorem108
4．Some Examples of the Dual Space of a Locally Convex Space114
5．Inductive Limits and the Space of Distributions116
CHAPTER Ⅴ Weak Topologies124
1．Duality124
2．The Dual of a Subspace and a Quotient Space128
3．Alaoglu's Theorem130
4．Reflexivity Revisited131
5．Separability and Metrizability134
6．An Application:The Stone-？ech Compactification137
7．The Krein-Milman Theorem141
8．An Application:The Stone-Weierstrass Theorem145
9．The Schauder Fixed Point Theorem149
10．The Ryll-Nardzewski Fixed Point Theorem151
11．An Application:Haar Measure on a Compact Group154
12．The Krein-Smulian Theorem159
13．Weak Compactness163
CHAPTER Ⅵ Linear Operators on a Banach Space166
1．The Adjoint of a Linear Operator166
2．The Banach-Stone Theorem171
3．Compact Operators173
4．Invariant Subspaces178
5．Weakly Compact Operators183
CHAPTER Ⅶ Banach Algebras and Spectral Theory for Operators on a Banach Space183
1．Elementary Properties and Examples187
2．Ideals and Quotients191
3．The Spectrum195
4．The Riesz Functional Calculus199
5．Dependence of the Spectrum on the Algebra205
6．The Spectrum of a Linear Operator208
7．The Spectral Theory of a Compact Operator214
8．Abelian Banach Algebras218
9．The Group Algebra of a Locally Compact Abelian Group223
CHAPTER Ⅷ C*-Algebras232
1．Elementary Properties and Examples232
2．Abelian C*-Algebras and the Functional Calculus in C*-Algebras236
3．The Positive Elements in a C*-Algebra240
4．Ideals and Quotients of C*-Algebras245
5．Representations of C*-Algebras and the Gelfand-Naimark-Segal Construction248
CHAPTER Ⅸ Normal Operators on Hilbert Space255
1．Spectral Measures and Representations of Abelian C*-Algebras255
2．The Spectral Theorem262
3．Star-Cyclic Normal Operators268
4．Some Applications of the Spectral Theorem271
5．Topologies on？(？)274
6．Commuting Operators276
7．Abelian von Neumann Algebras281
8．The Functional Calculus for Normal Operators:The Conclusion of the Saga285
9．Invariant Subspaces for Normal Operators290
10．Multiplicity Theory for Normal Operators:A Complete Set of Unitary lnvariants293
CHAPTER Ⅹ Unbounded Operators303
1．Basic Properties and Examples303
2．Symmetric and Self-Adjoint Operators308
3．The Cayley Transform316
4．Unbounded Normal Operators and the Spectral Theorem319
5．Stone's Theorem327
6．The Fourier Transform and Differentiation334
7．Moments343
CHAPTER Ⅺ Fredholm Theory347
1．The Spectrum Revisited347
2．Fredholm Operators349
3．The Fredholm Index352
4．The Essential Spectrum358
5．The Components of？362
6．A Finer Analysis of the Spectrum363
APPENDIX A Preliminaries369
1．Linear Algebra369
2．Topology371
APENDIX B The Dual of Lp(μ)375
APPENDIX C The Dual of C0(X)378
Bibliography384
List of Symbols391
Index395