Nonlinear maps preserving the reduced minimum modulus of operators

Let X and Y be infinite-dimensional complex Banach spaces, and let B(X) (resp. B(Y)) denote the algebra of all bounded linear operators on X (resp. on Y). We describe bijective bicontinuous maps φ from B(X) to B(Y) satisfyingγ(φ(S±φ(T)))=γ(S±T) for all S,T∈B(X), where γ(T) is the reduced minimum modulus of an operator T. An analogue result for the finite-dimensional case is obtained.