PERTURBATION BOUNDS FOR THE MOORE-PENROSE METRIC GENERALIZED INVERSE IN SOME BANACH SPACES

Let X,Y be Banach spaces, and let T, delta T : X -> Y be bounded linear operators. Put T = T + delta T. In this article, utilizing the gap between closed subspaces and the perturbation bounds of metric projections, we first present some error estimates of the upper bound of parallel to T-M-T-M parallel to in L-p (1 < p < +infinity) spaces. Then, by using the concept of strong uniqueness and modulus of convexity, we further investigate the corresponding perturbation bound parallel to T-M - T-M parallel to in uniformly convex Banach spaces.