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

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

2008-08-06

arxiv.org/abs/0808.0835v1

Mathematics

Operator Algebras

16 pages, 2 figures

Scientific paper

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.

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