泛函分析教程

图书标准信息

• 作者 J.B.Conway 编
• 出版社 世界图书出版公司
• 出版时间 2003-06
• 版次 2
• ISBN 9787506259514
• 定价 39.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 399页

【内容简介】

CHAPTERIHilbertSpaces、CHAPTERⅡOperatorsonHilbertSpace、CHAPTERⅢBanachSpaces、CHAPTERIVLocallyConvexSpaces、CHAPTERVWeakTopologies、CHAPTERⅥLinearOperatorsonaBanachSpace、CHAPTERⅦBanachAgebrasandSpectralTheoryforOperatorsonaBanachSpace、CHAPTERⅧC-Algebras、CHAPTERⅨNormalperatorsonHilbertSpace、CHAPTERⅩUnboundedOperators、
CHAPTERⅪFredholmTheory等。

【目录】

Preface
PrefacetotheSecondEdition
CHAPTERIHilbertSpaces
1.ElementaryPropertiesandExamples
2.Orthogonality
3.TheRieszRepresentationTheorem
4.OrthonormalSetsofVectorsandBases
5.IsomorphicHilbertSpacesandtheFourierTransformfortheCircle
6.TheDirectSumofHilbertSpaces

CHAPTERⅡOperatorsonHilbertSpace
1.ElementaryPropertiesandExamples
2.TheAdjointofanOperator
3.ProjectionsandIdempotents;InvariantandReducingSubspaces
4.CompactOperators
5.*TheDiagonalizationofCompactSelf-AdjointOperators
6.*AnApplication:Sturm-LiouvilleSystems
7.*TheSpectralTheoremandFunctionalCalculusforCompactNormalOperators
8.*UnitaryEquivalenceforCompactNormalOperators

CHAPTERⅢBanachSpaces
1.ElementaryPropertiesandExamples
2.LinearOperatorsonNormedSpaces
3.FiniteDimensionalNormedSpaces
4.QuotientsandProductsofNormedSpaces
5.LinearFunctionals
6.TheHahn-BanachTheorem
7.*AnApplication:BanachLimits
8.*AnApplication:Runge'sTheorem
9.*AnApplication:OrderedVectorSpaces
1.TheDualofaQuotientSpaceandaSubspace
11.ReflexiveSpaces
12.TheOpenMappingandClosedGraphTheorems
13.ComplementedSubspacesofaBanachSpace
14.ThePrincipleofUniformBoundedness

CHAPTERIVLocallyConvexSpaces
1.ElementaryPropertiesandExamples
2.MetrizableandNormableLocallyConvexSpaces
3.SomeGeometricConsequencesoftheHahn-BanachTheorem
4.*SomeExamplesoftheDualSpaceofaLocallyConvexSpace
5.*InductiveLimitsandtheSpaceofDistributions

CHAPTERVWeakTopologies
1.Duality
2.TheDualofaSubspaceandaQuotientSpace
3.Alaoglu'sTheorem
4.ReflexivityRevisited
5.SeparabilityandMetrizability
6.*AnApplication:TheStone-techCompactification
7.TheKrein-MilmanTheorem
8.AnApplication:TheStone-WeierstrassTheorem
9.*TheSchauderFixedPointTheorem
10.*TheRyll-NardzewskiFixedPointTheorem
11.*AnApplication:HaarMeasureonaCompactGroup
12.*TheKrein-SmulianTheorem
13.*WeakCompactness

CHAPTERVILinearOperatorsonaBanachSpace
CHAPTERVIIBanachAgebrasandSpectralTheoryforOperatorsonaBanachSpace
CHAPTERVIIIC-Algebras
CHAPTERIXNormalOperatorsonHilbertSpace
CHAPTERXUnboundedOperators
CHAPTERXIFredholmTheory
APPENDIXA
APPENDIXB
APPENDIXC
Bibliography
ListofSymbols
Index