" C*-approximation theory has provided the foundation for many of the most important
conceptual breakthroughs and applications of operator algebras. This book systematically …

We prove that the normalizer of any diffuse amenable subalgebra of a free group factor L (𝔽
r) generates an amenable von Neumann subalgebra. Moreover, any II₁ factor of the form …

We consider amalgamated free product II1 factors M= M 1* BM 2* B… and use
“deformation/rigidity” and “intertwining” techniques to prove that any relatively rigid von …

We prove that for any free ergodic probability measure-preserving action F n↷(X, μ) of a free
group on n generators F n, 2≤ n≤∞, the associated group measure space II1 factor …

We prove that if a countable group $\Gamma $ contains infinite commuting subgroups $ H,
H'\subset\Gamma $ with $ H $ non-amenable and $ H'$“weakly normal” in $\Gamma $, then …

We prove that for any free ergodic probability measure preserving action Γ→(X, μ) of a non-
elementary hyperbolic group, or a lattice in a rank one simple Lie group, the associated …

We study the C*-algebras and von Neumann algebras associated with the universal discrete
quantum groups. They give rise to full prime factors and simple exact C*-algebras. The main …

We introduce the notion of L 2-rigidity for von Neumann algebras, a generalization of
property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the …

We introduce the notion of proper proximality for finite von Neumann algebras, which
naturally extends the notion of proper proximality for groups. Apart from the group von …

R.–Ozawa a montré dans [21] que, pour un groupe cci hyperbolique, le facteur de type II1
associé est solide. En devéloppant une nouvelle approche, qui combine les méthodes de …