Journal article
Monic representations of the Cuntz algebra and Markov measures
Journal of functional analysis, Vol.267(4), pp.1011-1034
08/15/2014
DOI: 10.1016/j.jfa.2014.05.016
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.
Details
- Title: Subtitle
- Monic representations of the Cuntz algebra and Markov measures
- Creators
- Dorin Ervin Dutkay - University of Central Florida, Department of Mathematics, 4000 Central Florida Blvd., P.O. Box 161364, Orlando, FL 32816-1364, USAPalle E.T Jorgensen - University of Iowa, Department of Mathematics, 14 MacLean Hall, Iowa City, IA 52242-1419, USA
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.267(4), pp.1011-1034
- DOI
- 10.1016/j.jfa.2014.05.016
- ISSN
- 0022-1236
- eISSN
- 1096-0783
- Publisher
- Elsevier Inc
- Grant note
- DOI: 10.13039/100000893, name: Simons Foundation, award: 228539
- Language
- English
- Date published
- 08/15/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9983985841202771
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