Title

Monic Representations Of The Cuntz Algebra And Markov Measures

Keywords

Cuntz algebras; Infinite product measures; Markov measures; Wavelet representation

Abstract

We study representations of the Cuntz algebras ON. While, for fixed N, the set of equivalence classes of representations of ON is known not to have a Borel cross section, there are various subclasses of representations which can be classified. We study monic representations of ON, that have a cyclic vector for the canonical abelian subalgebra. We show that ON has a certain universal representation which contains all positive monic representations. A large class of examples of monic representations is based on Markov measures. We classify them and as a consequence we obtain that different parameters yield mutually singular Markov measure, extending the classical result of Kakutani. The monic representations based on the Kakutani measures are exactly the ones that have a one-dimensional cyclic Si*-invariant space. © 2014 Elsevier Inc.

Publication Date

8-15-2014

Publication Title

Journal of Functional Analysis

Volume

267

Issue

4

Number of Pages

1011-1034

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jfa.2014.05.016

Socpus ID

84902543470 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84902543470

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