Graph C*-algebras, branching systems and the Perron-Frobenius operator

Original · EN

In this paper we show how to produce a large number of representations of a graph C*-algebra in the space of the bounded linear operators in L²(X,μ). These representations are very concrete and, in the case of graphs that satisfy condition (K), we use our techniques to realize the associated graph C*-algebra as a subalgebra of the bounded operators in L²(R). We also show how to describe some Perron-Frobenius operators in L¹(X,μ), in terms of the representations we associate to a graph.