MAPS PRESERVING JORDAN AND ⁎-JORDAN TRIPLE PRODUCT ON OPERATOR ⁎-ALGEBRAS

Abstract

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 antimultiplicativity 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.