## Weakly Exact von Neumann Algebras and Amalgamated Free Products

### Kai Toyosawa; Vanderbilt University

Weak exactness for von Neumann algebras was first introduced by Kirchberg in 1995 as an analogue of exactness in the setting of C$^*$-algebras. In this talk, I will show that the amalgamated free product of weakly exact von Neumann algebras is again weakly exact. The proof involves a universal property of Toeplitz-Pimsner algebras and a locally convex topology on bimodules of von Neumann algebras, which is used to characterize weak exactness.

To participate in the seminar remotely via Zoom, go to https://uiowa.zoom.us/j/95316149275