C*代数和W*代数

1.GeneralTheory

1.1.DefinitionsofC*-AlgebrasandW*-Algebras

1.2.CommutativeC*-Algebras

1.3.StoneanSpaces

1.4.PositiveElementsofaC*-Algebra

1.5.PositiveLinearFunctionaisonaC*-Algebra

1.6.ExtremePointsintheUnitSphereofaC*-Algebra

1.7.TheWeakTopologyonaW*-Algebra

1.8.VariousTopologiesonaW*-Algebra

1.9.KaplanskysDensityTheorem

1.10.IdealsinaW*-Algebra

1.11.SpectralResolutionofSelf-AdjointElementsinaW*-Algebra

1.12.ThePolarDecompositionofElementsofaW*-Algebra

1.13.LinearFunctionalsonaW*-Algebra

1.14.PolarDecompositionofLinearFunctionalsonaW*-Algebra

1.15.ConcreteC*-AlgebrasandW*-Algebras

1.16.TheRepresentationTheoremsforC*-AlgebrasandW*-Algebras

1.17.TheSecondDualofaO-Algebra

1.18.CommutativeW*-Algebras

1.19.TheC*-AlgebraCofallCompactLinearOperatorsonaHilbertSpace

1.20.TheCommutationTheoremofyonNeumann

1.21.*-RepresentationsofC*-Algebras，1

1.22.TensorProductsofC*-AlgebrasandW*-Algebras

1.23.TheInductiveLimitandInfiniteTensorProductofC*-Algebras

1.24.Radon-NikodymTheoremsinW*-Algebras

2.ClassificationofW*-Algebras

2.1.EquivalenceofProjectionsandtheComparabilityTheorem

2.2.ClassificationofW*-Algebras

2.3.TypeIW*-Algebras

2.4.FiniteW*-Algebras

2.5.TracesandCriterionsofTypes

2.6.TypesofTensorProductsofW*-Algebras

2.7.*-RepresentationsofC*-AlgebrasandW*-Algebras，2

2.8.TheCommutationTheoremofTensorProducts

2.9.SpatialIsomorphismsofW*-Algebras

3.DecompositionTheory

3.1.DecompositionsofStates(Non-SeparableCases)

3.2.ReductionTheory(Space-Free)

3.3.DirectIntegralofHilbertSpaces

3.4.DecompositionofStates(SeparableCases)

3.5.CentralDecompositionofStates(SeparableCases)

4.SpecialTopics

4.1.DerivationsandAutomorphismsofC*-AlgebrasandW*-Algebras

4.2.ExamplesofFactors，1(GeneralConstruction)

4.3.ExamplesofFactors，2(UncountableFamiliesofTypesⅡ1，ⅡandⅢ

4.4.ExamplesofFactors，3(OtherResultsandProblems)

4.5.GlobalW*-Algebras(Non-Factors)

4.6.TypeIC*-Algebras

4.7.OnaStone-WeierstrassTheoremforC*-Algebras

Bibliography

SubjectIndex

ListofSymbols

　　本书是Springer经典数学教材系列之一。该系列包含已出版的400多本教材，许多已经被奉为经典并该科目的标准参考书。该书对vonNeumann代数理论给出了全面而详细的介绍。几乎包含该科目的所有基本结果。对于初学着和专家来说本书都是一本非常难得的参考书。　　读者对象：数学专业的研究生和相关专业的科研人员。