Spaceability and operator ideals

Let I1 and I2 be arbitrary operator ideals in the sense of Pietsch and E and F be Banach spaces such that the set I1(E,F){set minus}I2(E,F) is non-empty. We give a quite general sufficient condition on the Banach spaces in order to obtain the spaceability of I1(E,F){set minus}I2(E,F). Some consequences are provided when considering the ideals of compact operators, strictly singular operators, finitely strictly singular operators and Schatten operator classes.