An amenable equivalence relation is generated by a single transformation
TLDR
In this article, it was shown that for any amenable non-singular countable equivalence relation R⊂X×X, there exists a nonsingular transformation T of X such that, up to a null set, any two Cartan subalgebras of a hyperfinite factor are conjugate by an automorphism.Abstract:
We prove that for any amenable non-singular countable equivalence relation R⊂X×X, there exists a non-singular transformation T of X such that, up to a null set:It follows that any two Cartan subalgebras of a hyperfinite factor are conjugate by an automorphismread more
Citations
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Entropy and isomorphism theorems for actions of amenable groups
TL;DR: In this paper, certains des resultats fondamentaux de la theorie des isomorphismes aux actions des groupes unimodulaires moyennables generaux.
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Operator Algebras: Theory of C*-Algebras and von Neumann Algebras
TL;DR: In this article, the authors present a model for operators on Hilbert Space, including C*-Algebras, Von Neumann Algebra, and K-Theory and Finiteness.
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Processes on Unimodular Random Networks
David Aldous,Russell Lyons +1 more
TL;DR: In this article, the authors investigate unimodular random networks and their properties via reversibility of an associated random walk and their similarities to unimmodular quasi-transitive graphs, and extend various theorems concerning random walks, percolation, spanning forests, and amenability.
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The Banach-Tarski paradox
TL;DR: In this article, the authors show how tilings of the hyperbolic plane can help us visualize the Banach-Tarski paradox, which is one of the most shocking results of mathematics.
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Compact metric spaces, Fredholm modules, and hyperfiniteness
TL;DR: In this paper, it was shown that the existence of a finitely summable unbounded Fredholm module (h, D) on a C* algebra A implies a trace state on A and that no such module exists on the C * algebra of a non amenable discrete group.
References
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Ergodic equivalence relations, cohomology, and von Neumann algebras. II
J. Feldman,Calvin C. Moore +1 more
Classification of injective factors
TL;DR: Nann et al. as mentioned in this paper presented a survey of the main lines of the investigation in the classification of factors, culminating in the Connes-Takesakl structure theory of type III factors.