m at h . O A ] 6 A ug 2 00 8 Perron - Frobenius operators and representations of the Cuntz - Krieger algebras for infinite matrices August 6 , 2008
نویسنده
چکیده
In this paper we extend work of Kawamura, see [3], for CuntzKrieger algebras OA 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 OA. 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.
منابع مشابه
The Perron-Frobenius operators, invariant measures and representations of the Cuntz-Krieger algebras
For a transformation F on a measure space (X,μ), we show that the Perron-Frobenius operator of F can be written by a representation (L2(X,μ), π) of the Cuntz-Krieger algebra OA associated with F when F satisfies some assumption. Especially, when OA is the Cuntz algebra ON and (L2(X,μ), π) in the above is some irreducible representation of ON , then there is an F -invariant measure on X which is...
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