Additive maps preserving Jordan zero-products on nest algebras Original Research Article

Let image and image be nest algebras associated with the nests image and image on Banach Spaces. Assume that image and image are complemented whenever N-=N and M-=M. Let image be a unital additive surjection. It is shown that Φ preserves Jordan zero-products in both directions, that is Φ(A)Φ(B)+Φ(B)Φ(A)=0left right double arrowAB+BA=0, if and only if Φ is either a ring isomorphism or a ring anti-isomorphism. Particularly, all unital additive surjective maps between Hilbert space nest algebras which preserves Jordan zero-products are characterized completely.