因子von Neumann代数中套子代数上Jordan同构的刻画
CHARACTERIZATIONS OF JORDAN ISOMORPHISM ON NEST SUBALGEBRAS OF FACTOR VON NEUMANN ALGEBRAS

本文研究了套子代数上由零积确定的子集中保Jordan积的线性映射与同构和反同构的关系.证明了若对任意的A, B ∈ algMβ且AB=0,有φ(A ？ B)=φ(A) ？ φ(B)成立,则φ是同构或反同构.其中, algMβ, algMγ是因子von Neumann代数M中的两个非平凡套子代数,φ:algMβ → algMγ是一个保单位线性双射.
This paper studied the relation between linear mappings preserving Jordan product in subset determined by zero product on nest subalgebras and isomorphism and anti isomorphism, and proved that if φ satisfies φ(A ？ B)=φ(A) ？ φ(B) for all A, B ∈ algMβ with AB=0, then φ is an isomorphism or an anti-isomorphism, where algMβ and algMγ be non-trivial nest subalgebras in the factor von Neumann algebra M, φ is a unital bijection