Annals of Functional Analysis

On graph algebras from interval maps

C. Correia Ramos, Nuno Martins, and Paulo R. Pinto

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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.

Article information

Ann. Funct. Anal., Volume 10, Number 2 (2019), 203-217.

Received: 16 March 2018
Accepted: 18 July 2018
First available in Project Euclid: 19 March 2019

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Mathematical Reviews number (MathSciNet)

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 37E05: Maps of the interval (piecewise continuous, continuous, smooth) 37B10: Symbolic dynamics [See also 37Cxx, 37Dxx]

graph C$^{\ast}$-algebra representation transition matrix interval map


Ramos, C. Correia; Martins, Nuno; Pinto, Paulo R. On graph algebras from interval maps. Ann. Funct. Anal. 10 (2019), no. 2, 203--217. doi:10.1215/20088752-2018-0019.

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