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.