Linear mappings preserving the diameter of the numerical range

Let H be a complex Hilbert space and let B(H) be the set of all bounded linear operators on H. For every A∈B(H), the numerical range of A is the set W(A)={〈Ax,x〉:x∈Hand‖x‖=1} and the diameter of W(A) is the number d(W(A))=sup⁡{|λ−μ|:λ,μ∈W(A)}. A mapping T:B(H)→B(H) is called a diameter preserver if d(W(T(A)))=d(W(A)) for all A∈B(H). In this article we give a characterization of surjective linear diameter preservers.