Perron-Frobenius operators and representations of the Cuntz-Krieger algebras for infinite matrices

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In this paper we extend work of Kawamura, see kawamura, for Cuntz-Krieger algebras O_A for infinite matrices A. We generalize the definition of branching systems, prove their existence for any given matrix A and show how they induce some very concrete representations of O_A. We use these representations to describe the Perron-Frobenius operator, associated to an nonsingular transformation, as an infinite sum and under some hypothesis we find a matrix representation for the operator. We finish the paper with a few examples.
16 pages, 2 figures

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Operator Algebras, Dynamical Systems, 47L99

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http://salesiana.dossiersoluciones.com/handle/123456789/166535

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0808.0835
 http://arxiv.org/abs/0808.0835

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arXiv