Strong skew commutativity preserving maps on von Neumann algebras

作者：Qi, Xiaofei; Hou, Jinchuan^*

来源：Journal of Mathematical Analysis and Applications, 2013, 397(1): 362-370.

DOI：10.1016/j.jmaa.2012.07.036

• Von Neumann algebras
• Prime rings
• General preserving maps
• Skew Lie products

Let M be a von Neumann algebra without central summands of type I-1. Assume that Phi : M -> M is a surjective map. It is shown that Phi is strong skew commutativity preserving (that is, satisfies Phi(A)Phi(B) - Phi(B)Phi(A)(*) = AB - BA(*) for all A, B is an element of M) if and only if there exists some self-adjoint element Z in the center of M with Z(2) = I such that Phi(A) = ZA for all A is an element of M. The strong skew commutativity preserving maps on prime involution rings and prime involution algebras are also characterized.

• 出版日期2013-1-1
• 单位太原理工大学; 山西大学