关于Saitō猜想  

On a Conjecture of Saitō

作　　者：张永平[1] 

机构地区：[1]陕西师范大学

出　　处：《数学进展》1989年第3期329-334,共6页Advances in Mathematics（China）

摘　　要：Hakeda在[1]中研究了c-代数中Jordan映射的可加性,设M和N为AW-代数,M→N被称为Jordan-映射,如果满足下述条件: (3)为双射,其中,x·y=1/2(xy+yx).In this paper, the additivity of Jordan maps on JBW algebras is studied. In [1], Saito conjectured that results in [1] can be translated to JBW algebra, this conjecture is proved positively.Main theorem. If M and N are JBW algebras, is a Jordan map from M to N, and if M has no Summand of type I , can be extended to a Jordan map from M iM to N iN, and is continuous on every associative subalgebra of M iM, then is additive.

关 键 词：Saito猜想 JBW代数 JORDAN映射 

分 类 号：O177.5[理学—数学]