On the Stable Perturbation and Nashed’s Condition for Generalized Inverses†
Jiu Ding, Qianglian Huang · Numerical Functional Analysis and Optimization · 2020
Let T be a bounded linear operator from a Banach space to a Banach space with closed range and let T¯=T+δT. Nashed’s condition is that (I+δTT+)−1T¯ 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.