Factoriality and the Connes invariant T(M) for free products of von Neumann algebras

TL;DR

This paper studies the factoriality and the Connes invariant T(M) for free products of von Neumann algebras, correcting previous errors and extending the scope of the results to include certain infinite-dimensional cases.

Contribution

It provides corrected proofs and extends results on factoriality and the Connes invariant T(M) for free products of von Neumann algebras, especially for type I_ algebras.

Findings

Corrected proofs for factoriality and T(M) in free products

Extended results to include type I_ algebras

Clarified scope of previous theorems

Abstract

This revised version corrects some substancial errors in the proofs. The old proofs were only valid for (finite dimensional) * (finite dimensional). The scope of the results remains the same, however for type I_\infty algebras, the results of the original version were incorrect.