Perturbation Analysis for Oblique Projection Generalized Inverses

In this paper, we introduce the notion of stable perturbation of a subspace in Banach space. Utilizing this notion and the gap between subspaces, we develop a perturbation analysis for the oblique projection generalized inverse when the operator T, the range and null space of the projectors have perturbations simultaneously and estimate an upper bound of parallel to(T) over bar (+)(p,Q) - T-p,Q(+)parallel to Our results are new and extend the related results on the perturbation analysis of the oblique projection generalized inverse.