Abstract
Let A and B be two unital C*-algebras. Denote by W(a) the numerical range of an element a is an element of A. We show that the condition W(ax) = W(bx),for all x is an element of A implies that a = b. Using this, among other results, it is proved that if phi : A -> beta is a surjective map such that W(phi(a)phi(b)phi(c)) = W(abc) for all a, b and c is an element of A, then phi(1) is an element of Z(B) and the map psi = phi(1)(2) phi is multiplicative.