Linear maps and additive maps that preserve operators annihilated by a polynomial

Let H, K be infinite-dimensional complex Hilbert spaces. And let p(t) be a complex polynomial with deg(p) 2. In this paper we give a sufficient and necessary condition for a surjective linear or additive map Φ :B(H)→B(K) to preserve operators annihilated by p in both directions and answer a question raised by Šemrl affirmatively.  2002 Elsevier Science (USA). All rights reserved.