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

摘要

Let A and B be two operator ?-rings such that A is prime. In this paper, we show that if the map Φ:A→B 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→B is bijective and preserves ?-Jordan triple product, then Ψ is a C-linear or conjugate C-linear ?-isomorphism.