论文标题
von Neumann代数的投影晶格之间的晶格同构
Lattice isomorphisms between projection lattices of von Neumann algebras
论文作者
论文摘要
将冯·诺伊曼（Von Neumann）的结果推广到II型$ _1 $ von Neumann代数上，我们表征了晶格同构，这是通过局部可测量运算符的本地代数之间的环形同构来在任意von Neumann代数的投影晶格之间。此外，当von Neumann代数没有II型直接求和时，我们对本地可测量的代数的环形同构的环形同构的完整描述。
Generalizing von Neumann's result on type II$_1$ von Neumann algebras, we characterize lattice isomorphisms between projection lattices of arbitrary von Neumann algebras by means of ring isomorphisms between the algebras of locally measurable operators. Moreover, we give a complete description of ring isomorphisms of locally measurable operator algebras when the von Neumann algebras are without type II direct summands.
