Unitary equivalence and reduced minimum modulus preservers

Let L(H) be the algebra of all bounded linear operators acting on an infinite-dimensional complex Hilbert space H, and denote by gamma(T) the reduced minimum modulus of any operator T is an element of L(H). We obtain the form of all bijective linear maps Phi on L(H) for which gamma(Phi(T)) = gamma(Phi(S)) whenever T, S is an element of L(H) are two operators equivalent by unitaries. We also obtain similar results when the reduced minimum modulus is replaced by the minimum modulus or the surjectivity modulus.