泛函分析教程
2003-6
北京世图
J.B.Conway
399
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CHAPTER I Hilbert Spaces、CHAPTER Ⅱ Operators on Hilbert Space、CHAPTER Ⅲ Banach Spaces、CHAPTER IV Locally Convex Spaces、CHAPTER V Weak Topologies、CHAPTER Ⅵ Linear Operators on a Banach Space、CHAPTER Ⅶ Banach Agebras and Spectral Theory for Operators on a Banach Space、CHAPTERⅧ C-Algebras、CHAPTER Ⅸ Normal perators on Hilbert Space、CHAPTER Ⅹ Unbounded Operators、 CHAPTER Ⅺ Fredholm Theory等。
PrefacePreface to the Second EditionCHAPTER I Hilbert Spaces 1.Elementary Properties and Examples 2.Orthogonality 3.The Riesz Representation Theorem 4.Orthonormal Sets of Vectors and Bases 5.Isomorphic Hilbert Spaces and the Fourier Transform for the Circle 6.The Direct Sum of Hilbert SpacesCHAPTER II Operators on Hilbert Space 1.Elementary Properties and Examples 2.The Adjoint of an Operator 3.Projections and Idempotents; Invariant and Reducing Subspaces 4.Compact Operators 5.* The Diagonalization of Compact Self-Adjoint Operators 6.* An Application: Sturm-Liouville Systems 7.* The Spectral Theorem and Functional Calculus for Compact Normal Operators 8.* Unitary Equivalence for Compact Normal OperatorsCHAPTER III Banach Spaces 1.Elementary Properties and Examples 2.Linear Operators on Normed Spaces 3.Finite Dimensional Normed Spaces 4.Quotients and Products of Normed Spaces 5.Linear Functionals 6.The Hahn-Banach Theorem 7.* An Application: Banach Limits 8.* An Application: Runge's Theorem 9.* An Application: Ordered Vector Spaces 1.The Dual of a Quotient Space and a Subspace 11.Reflexive Spaces 12.The Open Mapping and Closed Graph Theorems 13.Complemented Subspaces of a Banach Space 14.The Principle of Uniform BoundednessCHAPTER IV Locally Convex Spaces 1.Elementary Properties and Examples 2.Metrizable and Normable Locally Convex Spaces 3.Some Geometric Consequences of the Hahn-Banach Theorem 4.* Some Examples of the Dual Space of a Locally Convex Space 5.* Inductive Limits and the Space of DistributionsCHAPTER V Weak Topologies 1.Duality 2.The Dual of a Subspace and a Quotient Space 3.Alaoglu's Theorem 4.Reflexivity Revisited 5.Separability and Metrizability 6.* An Application: The Stone-t ech Compactification 7.The Krein-Milman Theorem 8.An Application: The Stone-Weierstrass Theorem 9.* The Schauder Fixed Point Theorem 10.* The Ryll-Nardzewski Fixed Point Theorem 11.* An Application: Haar Measure on a Compact Group 12.* The Krein-Smulian Theorem 13.* Weak CompactnessCHAPTER VI Linear Operators on a Banach SpaceCHAPTER VII Banach Agebras and Spectral Theory for Operators on a Banach SpaceCHAPTER VIII C-AlgebrasCHAPTER IX Normal Operators on Hilbert SpaceCHAPTER X Unbounded OperatorsCHAPTER XI Fredholm TheoryAPPENDIX AAPPENDIX BAPPENDIX CBibliographyList of SymbolsIndex
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这是部非常经典的泛函分析教程,值得学习
看了这本书,在看其他的泛函分析教程,真是觉得相形见绌.让人感慨!
该书理论完整系统,行文优雅,定理证明严谨,简洁,明快。是国内外泛函分析学习研究的主要参考书。
老师让买的,挺深的,适合泛函一基础扎实的人
很好的教材,感觉比起国内的教材看着舒服,还是有些英文看不懂。
这本书还是比较有特点的,就是习题没答案。
这套GTM丛书质量极高,建议出版社出个套装。
帮室友买的,他很喜欢,说质量不错!!!
喜欢,好书,
内容比较全面,读起来也清楚明白,比较舒服。先 Hilbert 后 Banach 。
书是老板叫买的,可是看不懂
老师推荐的,说是世界级教材
挺好的书,包装精细。书本身也很好,适合所有专业的人阅读。
送货那天下雨书湿了!
内容难易程度适中,适合阅读
gtm有些书印刷质量不好,但是这一本却很不错,我是在图书馆先看到这么书才决定买的。另外,内容很全面,比较适合学算子代数的入门吧。
不错,没有想到世界图书出版公司出这本书
书的编排不错~
老师推荐教材,没的说的
这本书非常好,难易适中,但是需要一些实分析的基础,内容比东大的那位要简单些,相对少些!
有两页纸破了
相比内容与定价,纸质的质量有点差
听说很经典!
大师的文笔,行云流水
希望书的印刷质量有待提高啊
都是英文的,慢慢看
J.BConway的书很好很好就是当当送来的纸张特别特别差我们图书馆也有这本书纸张就比当当的不知道好多少