Graph Algebras as Subalgebras of the Bounded Operators in $L_2(\R)$

Details Graph Algebras as Subalgebras of the Bounded Operators in $L_2(\R)$ Graph Algebras as Subalgebras of the Bounded Operators in $L_2(\R)$

2009-08-07

arxiv.org/abs/0908.1055v1

Mathematics

Operator Algebras

18 pages, 5 figures

Scientific paper

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 $L^2(X,\mu)$. 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 $L^2(\R)$. We also show how to describe some Perron-Frobenius operators in $L^1(X,\mu)$, in terms of the representations we associate to a graph.

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