交换的实W~*-代数

本文指出，交换的（复）Ｗ 代数的大部分结果对于实情形仍然成立，自然有周期为２同胚的差别．此外，不同于复情形，可分实Ｈｉｌｂｅｒｔ空间中不包含任何极小投影的交换实ＶＮ代数同构于Ｌ∞（［０，１］），Ｌ∞ｒ（［０，１］）或Ｌ∞（［０，１］）Ｌ∞ｒ（［０，１］）．

Abelian Real W * algebras

In this paper, we point out that most results on abelian (complex) W * algebras hold in the real case. Of course, there are differences in homeomorphisms of period 2. Moreover, an abelian real Von Neumann algebra containing no any minimal projection on a separable real Hilbert space is * isomorphic to L ∞ r() (all real functions in L ∞() , or L ∞() (as a real W * algebra), or L ∞ r()L ∞ () (as a real W * -algebra), and it is different from the complex case.