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1、LectureNotesinMathematics1820Editors:J.--M.Morel,CachanF.Takens,GroningenB.Teissier,Paris3BerlinHeidelbergNewYorkHongKongLondonMilanParisTokyoFumioHiaiHidekiKosakiMeansofHilbertSpaceOperators13AuthorsFumioHiaiGraduateSchoolofInformationSciencesTohokuUn
2、iversityAoba-ku,Sendai980-8579Japane-mail:hiai@math.is.tohoku.ac.jpHidekiKosakiGraduateSchoolofMathematicsKyushuUniversityHigashi-ku,Fukuoka812-8581Japane-mail:kosaki@math.kyushu-u.ac.jpCataloging-in-PublicationDataappliedforBibliographicinformationpub
3、lishedbyDieDeutscheBibliothekDieDeutscheBibliothekliststhispublicationintheDeutscheNationalbibliografie;detailedbibliographicdataisavailableintheInternetathttp://dnb.ddb.deMathematicsSubjectClassification(2000):47A30,47A64,15A60ISSN0075-8434ISBN3-540-4
4、0680-8Springer-VerlagBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofi
5、lmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer-Verlag.Violationsareliab
6、leforprosecutionundertheGermanCopyrightLaw.Springer-VerlagBerlinHeidelbergNewYorkamemberofBertelsmannSpringerScience+BusinessMediaGmbHhttp://www.springer.decSpringer-VerlagBerlinHeidelberg2003PrintedinGermanyTheuseofgeneraldescriptivenames,registeredn
7、ames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Typesetting:Camera-readyTEXoutputbytheauthorSPIN:1094963441/3142/du-54
8、3210-Printedonacid-freepaperPrefaceRoughlyspeakingtwokindsofoperatorand/ormatrixinequalitiesareknown,ofcoursewithmanyimportantexceptions.Operatorsadmitseveralnaturalnotionsoforders(suchaspositivesemidefinitenessorder,somemajorizationorde
