The Perron-Frobenius operators, invariant measures and representations of the Cuntz-Krieger algebras

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

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 infini...

Radon–nikodym Representations of Cuntz–krieger Algebras and Lyapunov Spectra for Kms States

We study relations between (H,β)–KMS states on Cuntz–Krieger algebras and the dual of the Perron–Frobenius operator L∗ −βH . Generalising the well– studied purely hyperbolic situation, we obtain under mild conditions that for an expansive dynamical system there is a one–one correspondence between (H,β)– KMS states and eigenmeasures of L∗ −βH for the eigenvalue 1. We then consider representation...

Bonn States on the Cuntz Algebras and P-adic Random Walk States on the Cuntz Algebras and P-adic Random Walk States on the Cuntz Algebras and P -adic Random Walk

We study Markov measures and a p-adic random walk with the use of states on the Cuntz algebras Op. Via the GNS-construction, these come from families of representations of Op. We prove that these representations reflect self-similarity especially well. In this paper we consider a Cuntz-Krieger type algebra where the adjacency matrix depends on a parameter q (q = 1 is the case of Cuntz-Krieger)....

Spectrum Properties of the Koopman and Frobenius-Perron Operators

Weighted Frobenius-Perron and Koopman operators