We prove a spectral theorem for bimodules in the context of graph C*-algebras. A bimodule over a suitable abelian algebra is determined by its spectrum (i.e., its groupoid partial order)iff it is generated by the Cuntz-Kriegerpartial isometries which it contains iff it is invariant under thegauge automorphisms. We study 1-cocycles on the Cuntz-Kriegergroupoid associated with a graph C*-algebra, obtaining results on wheninteger valued or bounded cocycles on the natural AF subgroupoidextend. To a finite graph with a total order, we associate a nest subalgebra of the graph C*-algebra and then determine its spectrum. This is used toinvestigate properties of the nest subalgebra. We give acharacterization of the partial isometries in a graph C*-algebra which normalize a naturaldiagonal subalgebra and use this to show that gauge invariantgenerating triangular subalgebras are classified by their spectra.
展开▼
