摘要

For von Neumann algebras M,N not isomorphic to c C circle plus C and without type I-2 summands, we show that for an order -isomorphism f : AbSub M -> Absub N between the posets of abelian von Neumann sub-algebras of M and N, there is a unique Jordan *-isomorphism g : M -> N with the image g[S] equal to f(S) for each abelian von Neumann subalgebra S of M. The converse also holds. This shows the Jordan structure of a von Neumann algebra not isomorphic to C circle plus C and without type I-2 summands is determined by the poset of its abelian subalgebras, and has implications in recent approaches to foundational issues in quantum mechanics.

  • 出版日期2016