Maps On A Von Neumann Algebra Preserving Self-Jordan Products And Semi*-Jordan Products

In this paper, we study the maps on von Neumann algebras preserving self-Jordan products or semi*-Jordan products. A and B be von Neumann algebras on complex Hilbert spaces H and K, respectively, and let Φ:Aâ†'B be a bijective map. Firstly, when A and B are factor von Neumann algebras and Φ preserves self-Jordan products, it is proved that Φ preserves positive operators and projection operators in both directions. Secondly, when dim (H)>1and dim(K)>1, A and B are factor von Neumann algebras, and Φ is an additive bijection, it is proved that Φ preserves self-Jordan products if and only if Φ is a*-algebraic(anti-algebraic) isomorphism or a conjugate*-algebraic(anti-algebraic) isomorphism. Finally, when A and B are von Neumann algebras with no central summands of type â… 1; dim (H)>1and dim(K)>1, and Φ preserves semi*-Jordan products, it is proved that Φ is an additive map.