lecture notes on c-algebras and quantum mechanics [jnl article] - n. lamdsman

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1、LectureNotesonC-AlgebrasandQuantumMechanicsDraft:8April1998N.P.LandsmanKorteweg-deVriesInstituteforMathematics,UniversityofAmsterdam,PlantageMuidergracht24,1018TVAMSTERDAM,THENETHERLANDSemail:npl@wins.uva.nlhomepage:http://turing.wins.uva.nl/npl/telephone:020-5256282

2、oce:Euclides218a2CONTENTS3Contents1Historicalnotes51.1Originsinfunctionalanalysisandquantummechanics................51.2Ringsofoperators(vonNeumannalgebras)......................51.3Reductionofunitarygrouprepresentations......................61.4Theclassicationoffact

3、ors...............................81.5C-algebras........................................112ElementarytheoryofC-algebras122.1Basicdenitions.....................................122.2Banachalgebrabasics..................................152.3CommutativeBanachalgebras...

4、..........................202.4CommutativeC-algebras................................252.5Spectrumandfunctionalcalculus............................282.6PositivityinC-algebras.................................302.7IdealsinC-algebras...................................32

5、2.8States...........................................352.9RepresentationsandtheGNS-construction......................372.10TheGel'fand-Neumarktheorem.............................392.11Completepositivity....................................402.12Purestatesandirreduciblere

6、presentations.......................432.13TheC-algebraofcompactoperators..........................472.14Thedoublecommutanttheorem............................543HilbertC-modulesandinducedrepresentations563.1Vectorbundles......................................563.2Hilb

7、ertC-modules....................................583.3TheC-algebraofaHilbertC-module........................613.4Moritaequivalence....................................633.5Rieelinduction.....................................653.6Theimprimitivitytheorem.................

8、..............673.7GroupC-algebras....................................683.8C-dynamicalsystemsandcrossedproducts....