On the Stable Perturbation and Nashed's Condition for Generalized Inverses†. (25th October 2020) - Ding, Jiu; Huang, Qianglian
Abstract: Let T be a bounded linear operator from a Banach space to a Banach space with closed range and let T ¯ = T + δ T . Nashed's condition is that ( I + δ T T + ) − 1 T ¯ maps the null space of T into the range of T . The stable perturbation means that the intersection of the range of T ¯ and the null space of the generalized inverse of T is {0}. We show that the stable perturbation is the same as Nashed's condition in the sense of duality.