Maps Preserving Numerical Range Of Tensor Products On M2(?)M2

LetΨ:M2(C)(?)â‘£M2(C)â†'M2(C)(?)M2(C)be a linear map.It is shown that ψ satisfies W(ψ(A(?)B))=W(A(?)B)for all A(?)B∈M2(C)(?)M2(C)if and only if there is a unitary matrix U∈M4(C)such that ψ (X)=Uψ(X)U*for all X∈M2(C)(?)M2(C),where ψ is one of the following maps:the identity,the transpose,id (?) T and T (?) id with T the transpose map.