Maps preserving Jordan and -Jordan triple product on operator -algebras

Let A and B be two operator -rings such that A is prime. In this paper, we show that if the map Φ:A is bijective and preserves Jordan or -Jordan triple product, then it is additive. Moreover, if Φ preserves Jordan triple product, we prove the multiplicativity or anti-multiplicativity of Φ. Finally, we show that if A and B are two prime operator -algebras, Ψ:A is bijective and preserves -Jordan triple product, then Ψ is a C-linear or conjugate C-linear -isomorphism.