%0 Journal Article
%T On non-commutative transfer operators and Radon-Nikodym derivatives
%A Carlos F. Lardizabal
%J Physics
%D 2012
%I arXiv
%X We study relations between non-commutative Ruelle transfer operators over the C$^*$-algebra $B(\mathcal{H})$ of linear bounded operators over separable Hilbert spaces $\mathcal{H}$ (infinite-dimensional) and other completely positive maps. Transfer operators possess a simple description in terms of the so called non-commutative Radon-Nikodym derivatives. We describe the problem of existence of a largest positive eigenvalue associated to a positive eigenfunction and uniform convergence of sequences of iterates of transfer operators over $B(\mathcal{H})$. Part of the proof related to the Ruelle-Perron-Frobenius theorem is obtained by adapting results from quantum spin chain analysis.
%U http://arxiv.org/abs/1205.1736v2