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1、杭州电子科技大学硕士学位论文ABSTRACTTheoryofoperatoralgebrasproducedinthe20thcentury,30's,isanextremelyimportantpartinthestudyoffunctionalanalysis.Itishasextensivecontactsandmutualpenetrationwithphysics,quantummechanics,non-commutativegeometry,linearsystems,controltheory,numbertheory,andotherimporta
2、ntbranchofmathematics.Alongwithothersubjectsintheapplicationofthistheoryhasmadesignificantprogress,andhasbecomeamatterofconcerninmodernmathematics.Inrecentyears,therehasbeenconsiderableinterestinstudyingwhichlinearmappingonoperatoralgebrasarederivations,thisareahasbeenextensivelystudie
3、dbymanyexpertsandscholarsathomeandabroadandhasmadealotofscientificresearchresults.In1990,thenotionoflocalderivationswasintroducedindependentlybyD.R.LarsonandR.V.Kadison.Alsointhisyear，LarsonprovedthateverylocalderivationonB(H)isaderivation,whereXisaBanachspace.In1990,Kadisonprovedthate
4、verynorm-continuouslocalderivationonVonNeumannalgebraisaderivation.Afterword,WuJing,LuShijieandLiPengtongshowedthateveryderivablemappingφat0withφ()I=0onnestalgebrasisaninnerderivation.From2007to2009，ZhuJunandXiongChangpinghaveprovedthat(1)everyinvertibleoperatoronnestalgebrasisanall-de
5、rivablepointforthestronglyoperatortopology.(2)⎡⎤I0E=⎢⎥（Iisanidentityoperator）isanall-derivablepointofthealgebraofall2×2⎣⎦00operatormatricesforthestronglytopology.(3)G∈TMisanall-derivablepointofTMifand22onlyifG≠0whereTMisthealgebraofallnn×uppertriangularmatrices.(4)GU∈2nisanall-derivabl
6、epointinUifandonlyifG≠0whereUisthealgebraofallnn×nnmatrices.In2009,LuFangyanhasprovedonconditionthatletAisanBanachalgebraandXisanleft(orright)invertibleinA,thenδisaJordanderivationifδiscontinuousandderivableatX.Alsointhisyear，JingWuhasprovedonconditionthatletHbeaHilbertspaceandB()Hstan
7、dsforthealgebraofallboundedlinearoperatorsonH,then0isageneralizedJordanall-derivablepointofB(H)ifHisinfinite-dimensional;foranyHilbertspaceH,hehasalsoshowedthatIisaJordanall-derivablepointofB()H.Enlightenedandguidedbytheseresults,weextendtheresultstothealgebraofall2×2matrices.Inthisp
