Toeplitz algebras arising from escape points of interval maps

Abstract

We generate a representation of the Toeplitz C∗-algebra TAf on a Hilbert space Hx that encodes the orbit of an escape point x∈I of a Markov interval map f, with transition matrix Af. This leads to a family of representations of TAf labeled by points in all intervals I. The underlying dynamics of the interval map are used in the study of this family.