Maps preserving the bi-skew Jordan product on factor von Neumann algebras

Abstract

Abstract Let 𝒜 {\mathcal{A}} and ℬ {\mathcal{B}} be two von Neumann algebras. In this paper, we show that a bijective unital map Φ : 𝒜 → ℬ {\Phi:\mathcal{A}\to\mathcal{B}} which preserves the bi-skew Jordan product is an additive ∗ {\ast} -isomorphism. Moreover, we show that Φ is a linear ∗ {\ast} -isomorphism or a conjugate linear ∗ {\ast} -isomorphism.