拓扑向量空间

　　As the first edition of this book has been well received through five printings over a period of more than thirty years， we have decided to leave the material of the first edition essentially unchanged - barfing a few necessary updates. On the other hand， it appeared worthwhile to extend the existing text by adding a reasonably informative introduction to C*-and W*-algebras. The theory of these algebras seems to be of increasing importance in mathematics and theoretical physics， while being intimately related to topological vector spaces and their orderings——the prime concern of this text.The authors wish to thank J. Schweizer for a careful reading of ChapterVI， and the publisher for their care and assistance.

暂缺《拓扑向量空间》作者简介

PrefacetotheSecondEdition
Preface
Prerequisites
A.SetsandOrder
B.GeneralTopology
C.LinearAlgebra
Ⅰ.TOPOLOGICALVECTORSPACESIntroducction
1 VectorSpaceTopologies
2 ProductSpaces，Subspaces，DirectSums，QuotientSpaces
3 TopologicalVectorSpacesofFiniteDimension
4 LinearManifoldsandHyperplanes
5 BoundedSets
6 Metrizability
7 Complexification
Exercises
Ⅱ.LOCALLYCONVEXTOPOLOGICALVECTORSPACESIntroducction
1 ConvexSetsandSemi-Norms
2 NormedandNormableSpaces
3 TheHahn-BanachTheorem
4 LocallyConvexSpaces
5 ProjectiveTopologies
6 InductiveTopologies
7 BarreledSpaces
8 BornologicalSpaces
9 SeparationofConvexSets
10 CompactConvexSets
Exerises
Ⅲ.LINEARMAPPINGSIntroducction
1 ContinuouslinearMapsandTopologicalHomomorphisms
2 BanachsHomomorphismTheorem
3 SpacesofLinearMappings
4 Equicontinuity.ThePrincipleofUniformBoundednessandtheBanach-SteinhausTheorem
5 BilinearMappings
6 TopologicalTensorProducts
7 NuclearMappingsandSpaces
8 ExamplesofNuclearSpaces
9 TheApproximationProperty.CompactMaps
Exercises
Ⅳ.DUALITYIntroducction
1 DualSystemsandWeakTopologies
2 ElementaryPropertiesofAdjointMaps
3 LocallyConvexTopologiesConsistentwithaGivenDuality.TheMackey-ArensTheorem
4 DualityofProjectiveandInductiveTopologies
5 StrongDualofaLocalyConvexSpace.Bidual.ReflexiveSpaces
6 DualCharacterizationofCompleteness，MetrizableSpaces.TheoremsofGrothendieck，Banach-Dieudonne，andKrein-Smulian
7 AdjointsofClosedLinearMappings
8 TheGeneralOpenMappingandClosedGraphTheorems
9 TensorProductsandNuclearSpaces
10 NuclearSpacesandAbsoluteSummability
11 WeakCompactness.TheoremsofEberleinandKrein
Exercises
Ⅴ.ORDERSTRUCTURES
Introduction
1 OrderedVectorSpacesovertheRealField
2 OrderedVectorSpacesovertheComplexField
3 DualityofConvexCones
4 OrderedTopologicalVectorSpaces
5 PositiveLinearFormsandMappings
6 TheOrderTopology
7 TopologicalVectorLattices
8 ContinuousFunctionsonaCompactSpace.Theorems
ofStone-WeierstrassandKakutani
Exercises
Ⅵ.C*-ANDW*-ALGEBRAS
Introduction
1 Preliminaries
2 C*-Algebras.TheGelfandTheorem
3 OrderStructureofaC*-Algebra
4 PositiveLinearForms.Representations
SProjectionsandExtremePoints
6 W*-Algebras
7 VonNeumannAlgebras.KaplanskysDensityTheorem
8 ProjecdonsandTypesofW*-Algebras
Exercises
Appendix.SPECTRALPROPERTIESOFPOSITIVEOPERATORS
Introduction
1 ElementaryPropertiesoftheResolvent
2 PringshelmsTheoremandItsConsequences
TABLEOFCONTENTS
3 ThePeripheralPointSpectrum
IndexofSymbols
Bibliography
Index