# An upgrading theorem for properly proximal von Neumann algebras

@inproceedings{Ding2022AnUT, title={An upgrading theorem for properly proximal von Neumann algebras}, author={Changying Ding and Srivatsav Kunnawalkam Elayavalli}, year={2022} }

. Using computations in the bidual of B ( L 2 M ) we develop a technique at the von Neumann algebra level to upgrade relative proper proximality to full proper proximality in the presence of some mixing and non co-amenability assumptions. This is used to classify subalgebras of L Γ where Γ is an inﬁnite group that is biexact relative to a ﬁnite family of subgroups { Λ i } i ∈ I such that each Λ i is almost malnormal in Γ. As an application we obtain an absorption theorem for free products in…

## One Citation

### First $\ell^2$-Betti numbers and proper proximality

- Mathematics
- 2022

. We show that for a countable exact group, having positive ﬁrst ℓ 2 -Betti number implies proper proximality in this sense of [BIP21]. This is achieved by showing a cocycle super-rigidty result for…

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