泛函分析教程

內(nèi)容概要

　　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。

書籍目錄

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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