The Radon-Nikodym problem for approximately proper equivalence relations

Details The Radon-Nikodym problem for approximately proper equivalence relations The Radon-Nikodym problem for approximately proper equivalence relations

2002-11-23

arxiv.org/abs/math/0211369v1

Mathematics

Operator Algebras

37 pages

Scientific paper

We study the Radon-Nikodym problem for approximately proper equivalence
relations and more specifically the uniqueness of certain Gibbs states. One of
our tools is a variant of the dimension group introduced in the study of AF
algebras. As applications, we retrieve sufficient conditions for the uniqueness
of traces on AF algebras and parts of the Perron-Frobenius-Ruelle theorem.

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