C. Correia Ramos, Nuno Martins, Paulo R. Pinto. Source: Annals of Functional Analysis, Volume 10, Number 2, 203--217.Abstract:
We produce and study a family of representations of relative graph algebras on Hilbert spaces that arise from the orbits of points of $1$ -dimensional dynamical systems, where the underlying Markov interval maps $f$ have escape sets. We identify when such representations are faithful in terms of the transitions to the escape subintervals.