泛函分析教程

　　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。

暂缺《泛函分析教程》作者简介

Preface
PrefacetotheSecondEdition
CHAPTERI
HilbertSpaces
1.ElementaryPropertiesandExamples
2.Orthogonality
3.TheRieszRepresentationTheorem
4.OrthonormalSetsofVectorsandBases
5.IsomorphicHilbertSpacesandtheFourierTransformfortheCircle
6.TheDirectSumofHilbertSpaces
CHAPTERII
OperatorsonHilbertSpace
1.ElementaryPropertiesandExamples
2.TheAdjointofanOperator
3.ProjectionsandIdempotents;InvariantandReducingSubspaces
4.CompactOperators
5.TheDiagonalizationofCompactSelf-AdjointOperators
6.AnApplication:Sturm-LiouvilleSystems
7.TheSpectralTheoremandFunctionalCalculusforCompactNormalOperators
8.UnitaryEquivalenceforCompactNormalOperators
CHAPTERIII
BanachSpaces
1.ElementaryPropertiesandExamples
2.LinearOperatorsonNormedSpaces
3.FiniteDimensionalNormedSpaces
4.QuotientsandProductsofNormedSpaces
5.LinearFunctionals
6.TheHahn-BanachTheorem
7.AnApplication:BanachLimits
8.AnApplication:Runge'sTheorem
9.AnApplication:OrderedVectorSpaces
10.TheDualofaQuotientSpaceandaSubspace
11.ReflexiveSpaces
12.TheOpenMappingandClosedGraphTheorems
13.ComplementedSubspacesofaBanachSpace
14.ThePrincipleofUniformBoundedness
CHAPTERIV
LocallyConvexSpaces
1.ElementaryPropertiesandExamples
2.MetrizableandNormableLocallyConvexSpaces
3.SomeGeometricConsequencesoftheHahn-BanachTheorem
4.SomeExamplesoftheDualSpaceofaLocallyConvexSpace
5.InductiveLimitsandtheSpaceofDistributions
CHAPTERV
WeakTopologies
1.Duality
2.TheDualofaSubspaceandaQuotientSpace
3.Alaoglu'sTheorem
4.ReflexivityRevisited
5.SeparabilityandMetrizability
6.AnApplication:TheStone-CechCompactification
7.TheKrein-MilmanTheorem
8.AnApplication:TheStone-WeierstrassTheorem
9.TheSchauderFixedPointTheorem
10.TheRyll-NardzewskiFixedPointTheorem
11.AnApplication:HaarMeasureonaCompactGroup
12.TheKrein-SmulianTheorem
13.WeakCompactness
CHAPTERVI
LinearOperatorsonaBanachSpace
1.TheAdjointofaLinearOperator
2.TheBanach-StoneTheorem
3.CompactOperators
4.InvariantSubspaces
5.WeaklyCompactOperators
CHAPTERVII
BanachAlgebrasandSpectralTheoryforOperatorsonaBanachSpace
1.ElementaryPropertiesandExamples
2.IdealsandQuotients
3.TheSpectrum
4.TheRieszFunctionalCalculus
5.DependenceoftheSpectrumontheAlgebra
6.TheSpectrumofaLinearOperator
7.TheSpectralTheoryofaCompactOperator
8.AbelianBanachAlgebras
9.TheGroupAlgebraofaLocallyCompactAbelianGroup
CHAPTERVIII
C*-Algebras
1.ElementaryPropertiesandExamples
2.AbelianC*-AlgebrasandtheFunctionalCalculusinC*-Algebras
3.ThePositiveElementsinaC*-Algebra
4.IdealsandQuotientsofC*-Algebras
5.RepresentationsofC*-AlgebrasandtheGelfand-Naimark-SegalConstruction
CHAPTERIX
NormalOperatorsonHilbertSpace
1.SpectralMeasuresandRepresentationsofAbelianC*-Algebras
2.TheSpectralTheorem
3.Star-CyclicNormalOperators
4.SomeApplicationsoftheSpectralTheorem
5.Topologieson()
6.CommutingOperators
7.AbelianyonNeumannAlgebras
8.TheFunctionalCalculusforNormalOperators:TheConclusionoftheSaga
9.InvariantSubspacesforNormalOperators
10.MultiplicityTheoryforNormalOperators:ACompleteSetofUnitaryInvariants
CHAPTERX
UnboundedOperators
1.BasicPropertiesandExamples
2.SymmetricandSelf-AdjointOperators
3.TheCayleyTransform
4.UnboundedNormalOperatorsandtheSpectralTheorem
5.Stone'sTheorem
6.TheFourierTransformandDifferentiation
7.Moments
CHAPTERXl
FredholmTheory
1.TheSpectrumRevisited
2.FredholmOperators
3.TheFredholmIndex
4.TheEssentialSpectrum
5.TheComponentsof
6.AFinerAnalysisoftheSpectrum
APPENDIXA
Preliminaries
1.LinearAlgebra
2.Topology
APENDIXB
TheDualofLp(u)
APPENDIXC
TheDualofCo(X)
Bibliography
ListofSymbols
Index