Von Neumann代数中套子代数上Jordan映射的可加性

Additivity of Elementary Maps on Nest Subalgebra of Von Neumann Algebra

设A是因子von Neumann代数中的套子代数,B为实数域R上的任一代数,从A到B的r-Jordan映射具有什么样的特殊性质是研究此类映射的重要方面,文章从代数出发,充分利用代数的本身特性,证明了从A到B的每一个r-Jordan映射都是可加映射.

Let A be the nest algebra factor of Von Neumann algebra, B be any of the algebras on the actual number R, r-Jordan maps＇ property from A to B was the key aspect of it. It was proved that any r-Jordan map from A to B was additive.