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1、AShortIntroductiontoPerturbationTheoryforLinearOperatorsTosioKatoAShortIntroductiontoPerturbationTheoryforLinearOperatorsSpringer-VerlagNewYorkHeidelbergBerlinTosioKatoDepartmentofMathematicsUniversityofCaliforniaBerkeley,CA94720USAAMSSubjectClassifications(1980):46-01,34-01,340
2、10,47-01,47A55LibraryofCongressCataloginginPublicationDataKato,Tosio,1917-Ashortintrod~ctiontoperturbationtheoryforlinearoperators"Slightlyexpandedreproductionofthefirsttwochapters(plusintroduction)of...Perturbationtheoryforlinearoperators"-Pref.Bibliography:p.Includesindex.1.Li
3、nearoperators.2.Perturbation(Mathematics)I.TitleQA329.2.K37251982515.7'24682-10505ThisbookisaslightlyexpandedversionofChapters1and2of:T.Kato,PerturbationTheoryforLinearOperators2nded.(GrundlehrendermathematischenWissenschaften132).Springer-Verlag,Berlin,1980.C1982bySpringer-Verl
4、agNewYorkInc.SoftcoverreprintofthehardcoverIstedition1982Allrightsreserved.NopartofthisbookmaybetranslatedorreproducedinanyformwithoutwrittenpermissionfromSpringer-Verlag,175FifthAvenue,NewYork,NY10010,USA.TypesettingbyBriihlscheUniversitatsdruckerei(FRG).PrintingandbindingbyR.R
5、.Donnelley&Sons,Harrisonburg,VA.987654321ISBN-13:978-1-4612-5702-8e-ISBN-13:978-1-4612-5700-4DOl:10.1007/978-1-4612-5700-4PrefaceThisbookisaslightlyexpandedreproductionofthefirsttwochapters(plusIntroduction)ofmybookPerturbationTheorytorLinearOperators,Grundlehrendermathematische
6、nWissenschaften132,Springer1980.Eversince,orevenbefore,thepublicationofthelatter,therehavebeensuggestionsaboutseparatingthefirsttwochaptersintoasinglevolume.Ihavenowagreedtofollowthesuggestions,hopingthatitwillmakethebookavailabletoawideraudience.Thosetwochapterswereintendedfrom
7、theoutsettobeacomprehen•sivepresentationofthosepartsofperturbationtheorythatcanbetreatedwithoutthetopologicalcomplicationsofinfinite-dimensionalspaces.Infact,manyessentialand.evenadvancedresultsinthetheoryhavenon•trivialcontentsinfinite-dimensionalspaces,althoughoneshouldnotforg
8、etthatsomepartsofthetheory,suchasthosepertainin
