Maps preserving bi-skew η-Jordan product on von Neumann algebras

Abstract

Let [Formula: see text] and [Formula: see text] be two von Neumann algebras such that [Formula: see text] is factor. In this paper, we suppose that [Formula: see text] from [Formula: see text] onto [Formula: see text] is bijective, unital and satisfies [Formula: see text] for all [Formula: see text] where [Formula: see text] is a nonzero scalar such that [Formula: see text]. Then, [Formula: see text] is additive ∗-isomorphism.