Non Kazhdan's groups and a new approximation property for tracial von Neumann algebras

TL;DR

This paper introduces a new approximation property for tracial von Neumann algebras, called weakly mixing approximation property, which is equivalent to the negation of Kazhdan's property (T) for certain groups and factors.

Contribution

It defines the weakly mixing approximation property and establishes its equivalence to the negation of Kazhdan's property (T) for specific algebraic structures.

Findings

Weakly mixing approximation property is introduced.

Equivalence to negation of Kazhdan's property (T) established.

Applicable to discrete groups and II$_1$ factors.

Abstract

We define a new approximation property for tracial von Neumann algebras, called \textit{weakly mixing approximation property} which, for discrete groups and II$_1$ factors, is equivalent to the negation of Kazhdan's property (T).