特征为2的素*-代数上强保持2-新积

Strong 2-new product preserving maps on prime *-algebras of characteristic 2

摘要: 设 \Re 是特征为2包含非平凡对称幂等元的单位素*-代数. 对 A,B \in \Re ，定义 A \cdot B\rm = AB + BA^* 为新积，(A \cdot B)_2\rm = (A \cdot (A \cdot B)) 为2-新积.设 \phi :\Re \to \Re 是满射. 对所有 A,B \in \Re ，如果 \phi 满足 (\phi (A) \cdot \phi (B))_2\rm = (A \cdot B)_2 当且仅当对所有 A \in \Re ，存在 \alpha \in C_S 且 \alpha ^3 = I 使得 \phi (A) = \alpha A，其中 I 是 \Re 的单位，C_S 是 \Re 的对称可延拓中心. 作为应用，得到了素 C^* 代数和因子von Neumann代数上保持上述性质映射的结构.

Abstract: Let \Re be a unital prime *-algebra of characteristic 2 containing a nontrivial symmetric idempotent. For A,B \in \Re, the new product and 2-new product are defined, respectively, by A \cdot B\rm = AB + BA^* and (A \cdot B)_2 = (A \cdot (A \cdot B)). Let \phi :\Re \to \Re be a surjective map. It is shown that \phi satisfies (\phi (A) \cdot \phi (B))_2\rm = (A \cdot B)_2 for all A,B \in \Re if and only if there exists \alpha \in C_S with \alpha ^3 = I such that \phi (A) = \alpha A for all A \in \Re , where C_S is the symmetric extend centroid of \Re . As an application, such maps on prime C^* algebras and factor von Neumann algebras are characterized.