Some new perturbation theorems for generalized inverses of linear operators in Banach spaces

et X,Y be Banach spaces and let T∈B(X,Y) be a linear operator with closed range R(T). We consider the perturbation problem for the bounded outer inverse, the bounded (2,3)-inverse, and the bounded generalized inverse of T with respect to the projectors. Some new perturbation theorems are given by the generalized Neumman lemma and the concept of stable perturbations in Banach spaces.