# Ultraproducts, QWEP von Neumann algebras and the Effros-Mar\'echal topology

### Hiroshi Ando (IHES Paris)

Tuesday 21st January, 2014 16:00-17:00 Maths 416

#### Abstract

Haagerup and Winslow studied topological properties of the
Polish space vN(H) of von Neumann algebras acting on a separable
infinite-dimensional Hilbert space H. Motivated by the work of Effros,
this topology was introduced by Mar\'echal.
Among other interesting results, they proved that Kirhchberg's QWEP
conjecture is equivalent to the assertion that the set F_inj of
injective factors on H is dense in vN(H), and moreover a II_1 factor M
on H is R^{\omega}-embeddable if and only if M is the Effros-Mar\'echal
limit of a sequence of injective factors. Based on the work of
Haagerup-Winslow and the recent work of the speaker and Haagerup on
ultraproducts, we will give new characterizations of QWEP von Neumann
algebras.

This is a joint work with Uffe Haagerup and Carl Winslow (University of
Copenhagen).