一類不可分解Banach空間上線性算子理論及有關(guān)問(wèn)題.pdf

1、1023723分類號(hào)U0C密級(jí)單位代碼10094謝4￡i；千菡丈孿博士學(xué)位論文一類不可分解Banach空間上線性算子理論及有關(guān)問(wèn)題蘇維鋼指導(dǎo)教師姓名：鐘懷杰教授專業(yè)名稱基礎(chǔ)數(shù)學(xué)研究方向：空間與算子理論學(xué)位授予單位河北師范大學(xué)答辯委員會(huì)主席評(píng)閱人串請(qǐng)學(xué)位級(jí)別：理學(xué)博士論文答辯日期：2006年Io日學(xué)位授予時(shí)間：二00六年九月一日AbstractTherearemainlythreeaspectsinthispaperFirstlyonth

2、ebasisofthenewtypeofBanachspacesz1introducedbyGonzaiezandHerrera，thetheoryoflinearoperators，stronglycont“1nuous(semi)Foupsandthepropertiesofcosinefamilyarestudiedonthe￡：一typeBanachspaces，theyaremaincontentsinthispaperOns

3、uchspaces：itisshownthatthe8pectr哪礦(砷of8boundedlinearoperatorThascomespecialproperties，forinstance，thereisanuniquepoint^rin礦(，r)suchthatT—ATIisaninessentialoperator；80mepropertiesofthespectrumoflinearoperators(notnecessar

4、ilybounded)areobtained；itisshownthateverywellboundedoperatorTcanberepresenteda8T茹MKhereAisscalarKi8acompactoperator；itisshownthatthefamilyofallRisszoperatorsisjusttheidealofallinessentialoperators；itisshownthatthegenerat

5、orofeveryCb—groupisnecessarilyaboundedoperator；thegeneratorsof僥semigroupsneednotbeboundedbyanexample；itisshownthatthegeneratorsofcertainclassesofOosemigroupsoftheoperatorssucha8Hermitianoperatorsandisometriesarealwaysbou

6、nded：somesufficientconditionsareobtainedunderwhichthegeneratorsofunanimouslybounded島semigroupsarebounded(inparticularlyonreflexivespaces)；theconstitutionofthespectrumofthegeneratorofanyCosemigroupisobtained；itisshownthat

7、thegeneratorofany島semigroupsatisfiesthespectralmappingtheorem；aspectralcharacterizationofstabilityforunanimouslyboundedCo—semigroupsisobtained，andanapplicationtothestabilitytheoremisgiven；itisshownthatthegeneratorofanyst

8、ronglycontinuous，nonquasianalyticcosinefamilyisnecessarilyaboundedoperatorOngeneralBanachspaces，aconstitutiverepresentationforawellboundedRieszoperatorisobtained80itisshownthateverywellboundedRieszoperatorisnecessarilyac

9、ompactoperatorSecondlytheconceptsoftheleft(right)BrowderspectrumofoperatorsareintroducedongeneralBanashspacestheintersectionrelationsbetweentheleft(right)BrowderspectrumoftheoperatorsandthatoftheoperatorTarestudiedwhen占a

10、ndTarequasisimilaritisshownthateverycomponentoftherightBrowderspectrumofSintersectswiththeleftBrowderspectrumofTThirdlyongeneralBanachspaces，somesufficientandnecessaryconditionsareobtainedunderwhichtheoperatorswithcomple

11、telyfiniteuscentsatisfytheWeyltheorem，andthesufficientconditionsareobtainedunderwhichtwoquasisimilaroperatorsbothsatisfytheWeyltheorem；itisshownthateveryoperatorwithcompletelyfiniteascentsatisfiestheBrowdertheoremKeyword