Injective real \(W^*\)-factors of the type \(\text{III}_\lambda, 0<\lambda<1\) (Q1128377)

The author studies real \(W^*\)-factors of type \(\text{III}_\lambda\) for \(0<\lambda<1\). In contrast to the complex case, it is known that there are two nonisomorphic real injective \(W^*\)-factors of type \(\text{III}_\lambda\) for \(0<\lambda< 1\). The author's main result is that one of these two nonisomorphic factors is hyperfinite while the other is not. Therefore injectivity and hyperfiniteness are different for real algebras whereas they coincide for complex algebras.