资源描述：
《Operator Algebras, Operator Theory and Applications》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、OperatorTheory:AdvancesandApplications,Vol.181,3–32c2008Birkh¨auserVerlagBasel/SwitzerlandSubalgebrasofGraphC*-algebrasStephenC.PowerAbstract.Igiveaself-containedintroductiontotwonovelclassesofnonselfad-jointoperatoralgebras,namelythegeneralisedanal
2、yticToeplitzalgebrasLG,associatedwiththe“Fockspace”ofagraphG,andsubalgebrasofgraphC*-algebras.ThesetwotopicsaresomewhatindependentbutinbothcasesIshallfocusonfundamentaltechniquesandproblemsrelatedtoclassifyingisomor-phismtypesandtotherecoveryofunderl
3、yingfoundationalstructures,betheygraphsorgroupoids.MathematicsSubjectClassification(2000).Primary47L40.Keywords.Operatoralgebras,directedgraphs.Contents1Introduction...........................................................32TheCuntzalgebras,intuitiv
4、ely.........................................73Toeplitzalgebrasforcountabledirectedgraphs.........................174SubalgebrasofOn......................................................225Appendix:Digraphalgebrasandlimitalgebras......................
5、...27References................................................................311.IntroductionIgiveaself-containedintroductiontotwonovelclassesofnonselfadjointoperatoralgebras,namelythegeneralisedanalyticToeplitzalgebrasLG,associatedwiththe“Fockspac
6、e”ofagraphG,andsubalgebrasofgraphC*-algebras.ThesetwotopicsaresomewhatindependentbutinbothcasesIshallfocusonfundamen-taltechniquesandproblemsrelatedtoclassifyingisomorphismtypesandtotherecoveryofunderlyingfoundationalstructures,betheygraphsorgroupoid
7、s.4S.C.Power1.1.GeneralitiesonoperatoralgebrasLetussetthescenewithabird’seyeviewofhowoperatoralgebras“comeabout”andcommentontheirmorphisms.IshalltakethetermoperatoralgebratomeanacomplexalgebraofboundedlinearoperatorsonaseparablecomplexHilbertspace.Fo
8、rexample,theoperatoralgebraAcouldbethesetofallcomplexsinglevariablepolynomialsinagivenoperatorT;thatisA={p(T)=aI+aT+···+aTn:p(z)=a1+az+···+azn}.01n01nOften,theoperatoralgebrasofinterestaremanufacturedbyspecifyingasetofgenerators(suchastheset{I,T}inth
