functional analysis

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1、FUNCTIONALANALYSIS1DouglasN.Arnold2References:JohnB.Conway,ACourseinFunctionalAnalysis,2ndEdition,Springer-Verlag,1990.GertK.Pedersen,AnalysisNow,Springer-Verlag,1989.WalterRudin,FunctionalAnalysis,2ndEdition,McGrawHill,1991.RobertJ.Zimmer,EssentialResultsofFunctionalAnalysis,Universit

2、yofChicagoPress,1990.CONTENTSI.Vectorspacesandtheirtopology...............................................2Subspacesandquotientspaces............................................4BasicpropertiesofHilbertspaces.........................................5II.LinearOperatorsandFunctionals....

3、..........................................9TheHahn–BanachTheorem..............................................10Duality..................................................................10III.FundamentalTheorems.......................................................14TheOpenMappingTheor

4、em.............................................14TheUniformBoundednessPrinciple......................................15TheClosedRangeTheorem..............................................16IV.WeakTopologies.............................................................18Theweaktopology...

5、....................................................18Theweak*topology......................................................19V.CompactOperatorsandtheirSpectra........................................22Hilbert–Schmidtoperators...............................................22Compactopera

6、tors.......................................................23SpectralTheoremforcompactself-adjointoperators......................26Thespectrumofageneralcompactoperator.............................28VI.IntroductiontoGeneralSpectralTheory......................................31Thespectru

7、mandresolventinaBanachalgebra.........................31SpectralTheoremforboundedself-adjointoperators......................351Theselecturenoteswerepreparedfortheinstructor’spersonaluseinteachingahalf-semestercourseonfunctionalanalysisatthebeginninggraduatelevelatPennState,inSpring19