C*代数入门(英文版)
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作者[美]艾文森 著
出版社世界图书出版公司
出版时间2009-08
版次1
装帧平装
货号阳木
上书时间2024-07-04
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- 品相描述:八五品
图书标准信息
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作者
[美]艾文森 著
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出版社
世界图书出版公司
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出版时间
2009-08
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版次
1
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ISBN
9787510005060
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定价
18.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
106页
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正文语种
英语
- 【内容简介】
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ThisbookgivesanintroductiontoC*-algebrasandtheirrepresentationsonHilbertspaces.Wehavetriedtopresentonlywhatwebelievearethemostbasicideas,assimplyandconcretelyaswecould.Sowheneveritisconvenient(anditusuallyis),HilbertspacesbecomeseparableandC*-algebrasbecomeGCR.Thispracticeprobablycreatesanimpressionthatnothingofvalueisknownaboutother*-algebras.Ofcoursethatisnottrue.Butinsofarasrepresentationsarecon-cerned,wecanpointtotheempiricalfactthattothisdaynoonehasgivenaconcreteparametricdescriptionofeventheineduciblerepresentationsofany*-algebrawhichisnotGCR.Indeed,thereismetamathematicalevidencewhichstronglysuggeststhatnooneeverwill(seethediscussionattheendofSection3.4).Occasionally,whentheideabehindtheproofofageneraltheoremisexposedveryclearlyinaspecialcase,weproveonlythespecialcaseandrelegategeneralizationstotheexercises.Ineffect,wehavesystematicallyeschewedtheBourbakitradition.Wehavealsotriedtotakeintoaccounttheinterestsofavarietyofreaders.Forexample,themultiplicitytheoryfornormaloperatorsiscontainedinSections2.Iand2.2.(itwouldbedesirablebutnotnecessarytoincludeSectionI.1aswell),whereassomeoneinterestedinBoreLstructurescouldread
- 【目录】
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Chapter1Fundamentals
1.1.OperatorsandC*-algebras
1.2.Twodensitytheorems
1.3.Ideals,quotients,andrepresentations
1.4.C*-algebrasofcompactoperators
1.5.CCRandGCRalgebras
1.6.StatesandtheGNSconstruction
1.7.Theexistenceofrepresentations
1.8.Orderandapproximateunits
Chapter2MultiplicityTheory
2.1.FromtypeItomultiplicity-free
2.2.CommutativeC*-algebrasandnormaloperators
2.3.Anapplication:type!vonNeumannalgebras
2.4.GCRalgebrasaretypeI
Chapter3BorelStructures
3.1.Polishspaces
3.2.Borelsetsandanalyticsets
3.3.Boreispaces
3.4.Crosssections
Chapter4FromCommutativeAlgebrastoGCRAlgebras
4.1.ThespectrumofaC*-algebra
4.2.Decomposableoperatoralgebras
4.3.RepresentationsofGCRalgebras
Bibliography
Index
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