Jordan zero-product preserving additive maps on operator algebras

Let Φ : A → B be an additive surjective map between some operator algebras such that AB + BA = 0 implies Φ(A)Φ(B) + Φ(B)Φ(A) = 0. We show that, under some mild conditions, Φ is a Jordan homomorphism multiplied by a central element. Such operator algebras include von Neumann algebras, C∗-algebras and standard operator algebras, etc. Particularly, if H and K are infinite-dimensional (real or complex) Hilbert spaces and A = B(H) and B = B(K), then there exists a nonzero scalar c and an invertible linear or conjugate-linear operator U : H →K such that either Φ(A) = cUAU−1 for all A ∈ B(H), or Φ(A) = cUA∗U−1 for all A ∈ B(H).  2005 Elsevier Inc. All rights reserved