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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.MathematicsSubjectClassi?cation(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
