All Questions

Does there exist any theorem which permits, under suitable hypotheses, to represent a particular complete orthomodular lattice as the projection lattice of a Type III von Neumann factor?

Let $A$ be a von Neumann algebra. Then a classic observation is that the set of projections $\Pi(A)$ is naturally a complete orthomodular lattice. Question 1: Is the construction $A \mapsto \Pi(A)$ a ...

Let $ M, N $ be von Neumann algebras, $ P $ (resp. $Q$) the projection lattice of $M$ (resp. $N$). Any isomorphism $ \varphi : M \to N $ on the level of involutive algebras induces an isomorphism $ \...