Von Neumann equivalence and group exactness

TL;DR

This paper proves that group exactness remains invariant under von Neumann equivalence, extending known invariance results from measure and W*-equivalence to a broader context.

Contribution

It establishes that group exactness is a von Neumann equivalence invariant, generalizing previous invariance results to a wider class of equivalences.

Findings

Group exactness is invariant under von Neumann equivalence.

This invariance extends previous results from measure and W*-equivalence.

The result broadens understanding of invariance properties in operator algebra theory.

Abstract

We will show that group exactness is a von Neumann equivalence invariant. This result generalizes the previously known fact stating that group exactness is invariant under measure equivalence and W*-equivalence.