Banach格上的緊與弱緊算子.pdf

1、西南交通大學碩士學位論文Banach格上的緊與弱緊算子姓名：向日光申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：陳滋利2001.6.1西南交通大學碩士研究生學位論文第1I頁AbstractBasedonthedefinitionoflatticeandtheRieszdecomposition，inthispaper，weconsideredsomeequalitiesandinequalitiesonlatticesoperationsi

2、nRieszspacesandthelawofregularoperatorsdefinedonRieszspacesforlatticeoperations；Examinedsomepropertiesandsomerelationsbetweenspecialoperatorssuchasorderprojections，latticehomomorphisms，intervalpreservingoperators，bandpre

3、servingoperators，theoperatorswhichpreservedisjointness，orthomorphismsandordercontinuousoperatorsProvidedasufficientandnecessaryconditionofdisjointnessforfiniterankoperatorsdefinedonRieszspacesandseveralequalitiesofoperat

4、ionsinlatticesAlloftheseaimattheresearchonsomepropertiesofcompactoperatorsandweaklycompactoperatorsBaseontheoryofcompactoperators，WemainlycheckedsomedominatingpropertiesandsomeapplicationsoncompactoperatorsEstablishedtwo

5、spacesofcompactoperatorsandprovedindetailthatthespacesaretheideal，bandrespectivelyThetheoryofweaklycompactoperatorsismainpartofthisthesisItincludedweaklycompactoperators，orderweaklycompactoperators，semicompactoperators，L

6、weaklycompactoperators，MweaklycompactoperatorsandoperatorswhichhaveordercontinuousnormFirstly，inthispaperwepointedoutsomenecessaryconditionsonwhichaoperatorisaweaklycompact，andaweaklycompactoperatoristhesameasacompactope

7、ratorwhenitisdefinedonIiorc0，systematicallyanalyzedweakcompactnessofmodulusofweaklycompactoperatorsandthestructureofthespacesofweaklycompactoperators(DedekindcompleteRisezspaces，normclosedorderidealandSOon)，furtherapplie

8、dthedominatingtheoriesofweaklycompactoperatorstopractice，anddiscussedsometiesbetweenweaklycompactoperatorsandspacesonwhichweaklycompactoperatorsaredefinedSupplementedsomepropertiesoforderweaklycompactoperatorsBasedonthet