We generate a representation of the Toeplitz -algebra on a Hilbert space that encodes the orbit of an escape point of a Markov interval map , with transition matrix . This leads to a family of representations of labeled by points in all intervals . The underlying dynamics of the interval map are used in the study of this family.
"Toeplitz algebras arising from escape points of interval maps." Banach J. Math. Anal. 11 (3) 536 - 553, July 2017. https://doi.org/10.1215/17358787-2017-0005