Perturbation analysis of generalized inverses of linear operators in Banach spaces Original Research Article

Let X1, X2 be two Banach spaces and T:X1→X2 be a bounded linear operator with a bounded generalized inverse T+. We study the perturbation problem of generalized inverse T+ and provide two new stability characterizations of generalized inverse. We also give a continuity characterization of Moore–Penrose inverse in Hilbert spaces. Our results are new even in the case of matrices.