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1、GraduateTextsinMathematics253EditorialBoardS.AxlerK.A.RibetGraduateTextsinMathematicsForothertitlespublishedinthisseries,gotohttp://www.springer.com/series/136BarbaraD.MacCluerElementaryFunctionalAnalysisABCBarbaraD.MacCluerDepartmentofMathematicsUniversityofVirginiaP.O.Box400137Ch
2、arlottesvilleVA22904-4137USAbdm3f@virginia.eduEditorialBoardS.AxlerK.A.RibetMathematicsDepartmentMathematicsDepartmentSanFranciscoStateUniversityUniversityofCalifornia,BerkeleySanFrancisco,CA94132Berkeley,CA94720-3840USAUSAaxler@sfsu.eduribet@math.berkeley.eduISBN978-0-387-85528-8:
3、e-ISBN978-0-387-85529-5:DOI:10.1007/978-0-387-85529-5LibraryofCongressControlNumber:2008937759MathematicsSubjectClassification(2000:46-01,47-01)°cSpringerScience+BusinessMedia,LLC2009Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthe
4、publisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowkn
5、ownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.Printedonacid-freepaperspringer.comToTom,Josh,andDav
6、idPrefaceFunctionalanalysisaroseintheearlytwentiethcenturyandgradually,conqueringonestrongholdafteranother,becameanearlyuniversalmathematicaldoctrine,notmerelyanewareaofmathematics,butanewmathematicalworldview.Itsappearancewastheinevitableconsequenceoftheevolutionofallofnineteenth-
7、centurymathematics,inparticularclassicalanalysisandmathematicalphysics.ItsoriginalbasiswasformedbyCantorstheoryofsetsandlinearalgebra.Itsexistenceansweredthequestionofhowtostategeneralprinciplesofabroadlyinterpretedanalysisinawaysuitableforthemostdiversesituations.A.M.Vershik([45],
8、p.438).Thistextevolvedfrom
