[Richard_V._Kadison,__John_R._Ringrose__(auth.)]_F(BookZa.org).pdf

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1、FUNDAMENTALSOFTHETHEORYOFOPERATORALGEBRASSPECIALTOPICSVOLUMEIIIElementaryTheory-AnExerciseApproachFUNDAMENTALSOFTHETHEORYOFOPERATORALGEBRASSPECIALTOPICSVOLUMEIIIElementaryTheory-AnExerciseApproachRichardV.KadisonJohnR.RingroseDepartmentofMathematicsSchoolofMathematicsUniversityofPennsylvaniaU

2、niversityofNewcastlePhiladelphia,PennsylvaniaNewcastleuponTyne,EnglandCOPYRIGHT©1991,byRICHARDV.KADISONSofcoverreprintofthehardcover1stedition1991ALLRIGHTSRESERVED.NOPARTOFTHISPUBLICATIONMAYBEREPRODUCEDORTRANSMITTEDINANYFORMORBYANYMEANS,ELECTRONICORMECHANICAL,INCLUDINGPHOTOCOPY,RECORDING,ORAN

3、YINFORMATIONSTORAGEANDRETRIEVALSYSTEM,WITHOUTPERMISSIONINWRITINGFROMRICHARDV.KADISON.THESTATEMENTSOFALLEXERCISES(©ACADEMICPRESS1983)APPEARWITHTHEPERMISSIONOFACADEMICPRESS.BIRKHAUSERBOSTON675MassachusettsAvenue,Cambridge,MA02139-3309LibraryofCongressCataloginginPublicationDataKadison,RichardV.

4、,7-25-25FundamentalsofthetheoryofoperatoralgebrasSpecialtopicsElementarytheory-anexerciseapproachIncludespreface,exercisegroupingsbibliography,index.1.Operatoralgebras.I.Ringrose,JohnR.II.TitlePrintedonacidfreepaper.ISBN-13:978-1-4612-7834-4e-ISBN-13:978-1-4612-3212-4DOl:10.1007/978-1-4612-32

5、12-4PrintedbyQuinn-Woodbine,Inc.,Woodbine,NewJersey987654321CONTENTSPrefaceVllContentsofVolumeIVIXExerciseGroupingsXlChapter1.LinearSpaces-Exercisesand1SolutionsChapter2.BasicsofHilbertSpaceand40LinearOperators-ExercisesandSolutionsChapter3.BanachAlgebras-Exercises84andSolutionsChapter4.Eleme

6、ntaryC*-AlgebraTheory139-ExercisesandSolutionsChapter5.ElementaryvonNeumann207AlgebraTheory-ExercisesandSolutionsBibliography263Index268PREFACEThesevolumesarecompanionstothetreatise;"FundamentalsoftheTheoryofOperatorAlgebras,"whichappearedasVolume100-IandIIintheseries,PureandAppliedMathematic

7、s,publishedbyAcademicPressin1983and1986,respectively.Asstatedintheprefacetothosevolumes,"Theirprimarygoalistoteachthesub•jectandleadthereadertothepointwherethevastrecentresearchliterature,bothinthesubjectproperandinitsmanyapplications,becomes