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1、LectureNotesinMathematics1820Editors:J.--M.Morel,CachanF.Takens,GroningenB.Teissier,Paris3BerlinHeidelbergNewYorkHongKongLondonMilanParisTokyoFumioHiaiHidekiKosakiMeansofHilbertSpaceOperators13AuthorsFumioHiaiGraduateSchoolofInformationSciencesTohokuUniversi
2、tyAoba-ku,Sendai980-8579Japane-mail:hiai@math.is.tohoku.ac.jpHidekiKosakiGraduateSchoolofMathematicsKyushuUniversityHigashi-ku,Fukuoka812-8581Japane-mail:kosaki@math.kyushu-u.ac.jpCataloging-in-PublicationDataappliedforBibliographicinformationpublishedbyDieD
3、eutscheBibliothekDieDeutscheBibliothekliststhispublicationintheDeutscheNationalbibliografie;detailedbibliographicdataisavailableintheInternetathttp://dnb.ddb.deMathematicsSubjectClassification(2000):47A30,47A64,15A60ISSN0075-8434ISBN3-540-40680-8Springer-Ver
4、lagBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andsto
5、rageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer-Verlag.ViolationsareliableforprosecutionundertheGerman
6、CopyrightLaw.Springer-VerlagBerlinHeidelbergNewYorkamemberofBertelsmannSpringerScience+BusinessMediaGmbHhttp://www.springer.decSpringer-VerlagBerlinHeidelberg2003PrintedinGermanyTheuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicatio
7、ndoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Typesetting:Camera-readyTEXoutputbytheauthorSPIN:1094963441/3142/du-543210-Printedonacid-freepaperPrefaceRoughly
8、speakingtwokindsofoperatorand/ormatrixinequalitiesareknown,ofcoursewithmanyimportantexceptions.Operatorsadmitseveralnaturalnotionsoforders(suchaspositivesemidefinitenessorder,somemajorizationorde
