Orthogonality preserving pairs of operators on Hilbert C0(Z)-modules

Suppose that Z is a locally compact Hausdorff space and Psi, Phi : E -> F are C-0(Z)-module maps between Hilbert C-0(Z)-modules such that for every x, y is an element of E, x perpendicular to y implies Psi(x) perpendicular to Phi(y). Then there exists a bounded complex-valued function phi on Z that is continuous on Z(E) = {z is an element of Z : < x, x > (z) not equal 0 forsome x is an element of E} and satisfies <Psi(x), Phi(y)> = phi . < x, y > on Z, for all x, y is an element of E.