MAPS PRESERVING MIXED JORDAN TRIPLE PRODUCT OF OPERATORS ON PRIME ALGEBRAS

Let \mathcal{A} and \mathcal{B}be unital prime algebras and \mathcal{A} contains a non-trivial idempotent P_۱.We consider a bijective map \phi: \mathcal{A} \rightarrow \mathcal{B} which satisfies\begin{equation*}\phi (A.BoA)= \phi (A). \phi(B)o \phi(A)\end{equation*}for every element A,B\in \mathcal{A}, where '.' is a usual product and "\circ" is a Jordan product.

Keywords:

Preserver problem , Fixed point , Jordan product