论文标题
II型$ _ \ infty $本地可测量操作员代数的戒指同构
Ring isomorphisms of type II$_\infty$ locally measurable operator algebras
论文作者
论文摘要
我们表明，对于II型$ _ \ indy $ _ \ von Neumann代数的本地可测量运算符代数之间的每个环同构，类似于真正的$^*$ - 同构。这与作者和Ayupov-Kudaybergenov的先前结果完全描述了本地可测量操作员的代数之间的环形同构，以及在没有有限I类型的von Neumann代数的一般代数的一般代数的一般代数的一般代数中的投影晶格之间的晶格同构。
We show that every ring isomorphism between the algebras of locally measurable operators for type II$_\infty$ von Neumann algebras is similar to a real $^*$-isomorphism. This together with previous results by the author and Ayupov--Kudaybergenov completely describes ring isomorphisms between the algebras of locally measurable operators as well as lattice isomorphisms between the projection lattices for a general pair of von Neumann algebras without finite type I direct summands.
