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1、FUNDAMENTALSOFTHETHEORYOFOPERATORALGEBRASVOLUMEIElementaryTheoryThisisavolumeinPUREANDAPPLIEDMATHEMATICSASeriesofMonographsandTextbooksEditors:SAMUELEILENBERGANDHYMANBASSAlistofrecenttitlesinthisseriesappearsattheendofthisvolume.FUNDAMENTALSOFTHETHEORYOFOPERATORALG
2、EBRASVOLUMEIElementaryTheoryRichardV.KadisonJohnR.RingroseDepartmentofMathematicsSchoolofMarhematicsUniversityofPennsylvaniaUniversityofNewcastlePhiladelphia,PennsylvaniaNewcastleuponTyne,England1983ACADEMICPRESSASubsidiaryofHarcourtBraceJovanovich,PublishersNewYor
3、kLondonParisSanDiegoSanFranciscoSiloPauloSydneyTokyoTorontoCOPYRIGHT@1983,BYACADEMICPRESS,INC.ALLRIGHTSRESERVED.NOPARTOFTHISPUBLICATIONMAYBEREPRODUCEDORTRANSMITTEDINANYFORMORBYANYMEANS,ELECTRONICORMECHANICAL,INCLUDINGPHOTOCOPY,RECORDING,ORANYINFORMATIONSTORAQEANDRE
4、TRIEVALSYSTEM,WITHOUTPERMISSIONINWRITINQFROMTHEPUBLISHER.ACADEMICPRESS,INC.111FifthAvenue,NewYork,NewYork10003UnitedKingdomEditionpublishedbyACADEMICPRESS,INC.(LONDON)LTD.24/28OvalRoad,LondonNWlIDXLibraryofCongressCataloginginPublicationDataKadison,RichardV.,dateFu
5、ndamentalsofthetheoryofoperatoralgebras.(Pureandappliedmathematics)Includesindex.1.Operatoralgebras.I.Ringrose,JohnR.11.Title.111.Series:Pureandappliedmathematics(AcademicPress)QA3.P8[QA326]512’.5582-13768ISBN0-12-393301-3(v.1)PRINTEDINTHEUNITEDSTATESOFAMERICAa3a4a
6、5869a7654321CONTENTSPrefaceviiContentsofVolumeI1xiiiChapter1.LinearSpaces1.1.Algebraicresults11.2.Lineartopologicalspaces121.3.Weaktopologies281.4.Extremepoints311.5.Norrnedspaces351.6.Linearfunctionalsonnormedspaces431.7.SomeexamplesofBanachspaces481.8.Linearopera
7、torsactingonBanachspaces591.9.Exercises65Chapter2.BasicsofHilbertSpaceandLinearOperators2.1.Innerproductsonlinearspaces752.2.Orthogonality852.3.Theweaktopology972.4.Linearoperators99Generaltheory100Classesofoperators1032.5.Thelatticeofprojections1092.6.Construction
8、swithHilbertspaces120Subspaces120Directsums121TensorproductsandtheHilbert-Schmidtclass125Matrixrepresentations1472.7.Unboundedlinearoperators1542
