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  • 拓扑向量空间(第2版)[平装]
  • 共2个商家     36.00元~38.40
  • 作者:舍费尔(Schaefer.H.H)(作者)
  • 出版社:世界图书出版公司;第2版(2009年4月1日)
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  • 包装:
  • ISBN:9787510004469

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    《拓扑向量空间(第2版)》是由世界图书出版公司出版的。

    作者简介

    作者:(英国) 舍费尔 (Schaefer.H.H)

    目录

    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 Banach'sHomomorphismTheorem
    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.Kaplansky'sDensityTheorem
    8 ProjecdonsandTypesofW*-Algebras
    Exercises

    Appendix.SPECTRALPROPERTIESOFPOSITIVEOPERATORS
    Introduction
    1 ElementaryPropertiesoftheResolvent
    2 Pringshelm'sTheoremandItsConsequences
    TABLEOFCONTENTS
    3 ThePeripheralPointSpectrum
    IndexofSymbols
    Bibliography
    Index

    序言

    The present book jS intended to be a systematic text on topological vector spaces and presupposes familiarity with the elements of general topology and linear algebra.The author has fclund it unnecessary to rederive these results. since they are equally basic for many other areas of mathematics,and every beginning graduate student iS likely to have made their acquaintance.Simi- larly,the elementary facts on Hilbert and Banach spaces are widely known and are not discussed in detail jn this book.which iS mainly addressed to those readers who have attained and wish to get beyond the introductory level.
    The book has its origin in courses given by the author at Washington State University,the University of Michigan,and the University of Tiibingen in the years l 958一l 963.At that time there existed no reasonably complete text on topological vector spaces in English.and there seemed to be a genuine need for a book on this SUbject.This situation changed in l 963 with the appearance of the book by Kelley,Namioka et a1.【l】which,through its many elegant proofs.has had some influence on the final draft of this manuscript.Yet the two books appear to be sufficiently difierent in spirit and SUbject matter to justify the publication of this manuscript;in particular,the present book includes a discussion of topological tensor products,nuclear spaces,ordered topological vector spaces.and an appendix on positive operators.The author is also glad to acknowledge the strong influence of Bourbaki,whose mono- graph【7】,【8】8 was(before the publication of K6the【5】)the only modern treatment of topological vector spaces in printed form.
    A feW words should be said about the organization of the book.There iS a preliminary chapter called“Prerequisites.”which iS a survey aimed at clarifving the terminology to be used and at recalling basic definitions and facts to the reader’S mind.Each of the five following chapters.as welI as the Appendix,iS divided into sections.In each section,propositions are marked U.V,where U iS the section number.

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