Banach Journal of Mathematical Analysis

Toeplitz algebras arising from escape points of interval maps

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

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Abstract

We generate a representation of the Toeplitz C*-algebra TAf on a Hilbert space Hx that encodes the orbit of an escape point xI 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.

Article information

Source
Banach J. Math. Anal., Volume 11, Number 3 (2017), 536-553.

Dates
Received: 19 April 2016
Accepted: 23 August 2016
First available in Project Euclid: 29 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1493431219

Digital Object Identifier
doi:10.1215/17358787-2017-0005

Mathematical Reviews number (MathSciNet)
MR3679895

Zentralblatt MATH identifier
1380.46049

Subjects
Primary: 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]
Secondary: 37B10: Symbolic dynamics [See also 37Cxx, 37Dxx] 37E05: Maps of the interval (piecewise continuous, continuous, smooth) 46L05: General theory of $C^*$-algebras

Keywords
Toeplitz algebra interval maps orbit representations

Citation

Correia Ramos, C.; Martins, Nuno; Pinto, Paulo R. Toeplitz algebras arising from escape points of interval maps. Banach J. Math. Anal. 11 (2017), no. 3, 536--553. doi:10.1215/17358787-2017-0005. https://projecteuclid.org/euclid.bjma/1493431219


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