∗∗-Jordan-triple multiplicative surjective maps on B(H)B(H)

Let HH be a Hilbert space and B(H)B(H) be the algebra of all bounded linear operators on HH. In this paper we obtain a structure theorem of maps preserving the ∗∗-Jordan-triple zero product on B(H)B(H). Then this is applied to give a full characterization of a surjective map Φ:B(H)→B(H)Φ:B(H)→B(H) satisfying Φ(AB∗A)=Φ(A)Φ(B)∗Φ(A)Φ(AB∗A)=Φ(A)Φ(B)∗Φ(A).