Abstract In 1967, Kadison asked “if\(N\) is a subfactor of the factor\(M\) for which\(N'\cap M\)
consists of scalars, will some maximal abelian*-subalgebra of\(N\) be a maximal abelian …

We show that for a countable exact group, having positive first ℓ 2-Betti number implies
proper proximality in this sense of [3]. This is achieved by showing a cocycle superrigidity …

We study several classes of Banach bimodules over a II 1 factor M, endowed with topologies
that make them “smooth” with respect to L p-norms implemented by the trace τ on M. Thus …

Let Mq (HR) be the q-Gaussian von Neumann algebra associated with a separable infinite
dimensional real Hilbert space HR where− 1< q< 1. We show that Mq (HR) ̸≃ M0 (HR) for …

In this paper, the notion of proper proximality (introduced by Boutonnet, Ioana, and Peterson
[Ann. Sci. Éc. Norm. Supér.(4) 54 (2021), 445–482]) is studied and classified in various …

We single out a large class of groups are 'rigid'. In particular, we provide an alternative
solution to a question of Popa that was recently answered by Ding, Kunnawalkam Elayavalli …

Using computations in the bidual of B (L 2 M) we develop a new technique at the von
Neumann algebra level to upgrade relative proper proximality to full proper proximality. This …

We introduce the notion of biexactness for general von Neumann algebras, naturally
extending the notion from group theory. We show that biexactness implies solidity for von …

We establish a hypertrace characterization of property (T) for II 1 factors: Given a II 1 factors
M, M does not have property (T) if and only if there exists a von Neumann algebra A with …

We give a simple and explicit proof that the free group $\mathbb {F} _2 $ admits a measure
equivalence embedding into any nonamenable locally compact second countable (lcsc) …