# 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 $\mathbb{B}(L^2M)$ 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 $L\Gamma$ where $\Gamma$ is an infinite group that is biexact relative to a finite family of subgroups $\{\Lambda_i\}_{i\in I}$ such that each $\Lambda_i$ is almost malnormal in $\Gamma$. As an application we obtain…

## 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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