算子矩陣的譜擾動(dòng).pdf

1、陜西師范大學(xué)碩士學(xué)位論文算子矩陣的譜擾動(dòng)姓名：李愿申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：杜鴻科20040401ThePerturbationsonSpectraofOperatorMatrix1ruanLiAbstractItiswellknownthatoperatormatrixisamatrixwithoperatorsasitselementsIntherecenttenyears，theproblemsONperturba

2、tionsofspectrumof2X2operatormatrix，especially2X2uppertriangularoperatormatrix，haveabsorbedmanyscholars，suchasHKDu，DSDjordjevic，JPan，JKHan，HYLee，WYLeeandSOonInthisarticle，westudytheproblemsonperturbationsofspectrumof2x2op

3、eratormatrix，especially2X2uppertriangularoperatormatrix，suchasleft(right)spectrum，left(right)essentialspectrumandleft(rightlWeylspectrumLet丸and_cbecomplexseparableHilbertspacesDenoteB(7／)andB(Jc，“)theBanachspacesofallthe

4、boundedlinearoperatorsOil71andfrom_Icinto“，respectivelyIfA∈B(w)，B∈B(E)，forC∈B(咒，咒)，letMedenotethe22uppertriangularoperatormatrix：廠AG、l0BJ‘Therearethreechaptersinthisarticle，andthemaincontentasfollows：Inthefirstchapter，we

5、havestudiedtheintersectionofleftspectrumofMc，when0isrestrictedonthesetofalltheoperatorswithclosedrangeBc(K，7／)，thesetofalltheleftinvertibleoperatorsBt(pc，咒)，thesetofallthecompactoperatorsK(瓦，咒)andthesetofalltheoperatorsw

6、ithfiniterangeF(￡，7／)，respectivelyWegivethecharacterizationsofthemAsaresult，wegetandnG∈B。(苊，n)al(Mc)=VICEBl(丘，n)at(Me)QceK(x：n)al(Mc)=QceF(丘，u)m(Mc)Andinthesecondchapter，wehavestudiedtheperturbationsofleft(right)essentia

7、lspectrum，andleft(right)WeylspectrumIfA∈B(7／)，B∈B(尼)，wegivethecompletecharacterizationsoftheintersectionofleft(right)essentialspectrumnc∈B㈣n)ate(Mc)(QCEB[K，咒)are(Mc))andtheintersectionofleft(right)Weylspectrumnc∈B(K。w)嘰“