Some new perturbation theorems for generalized inverses of linear operators in Banach spaces (Q603126)

Motivated by \textit{J.\,Ding} [Linear Algebra Appl.\ 362, 229--235 (2003; Zbl 1044.47011)], the authors investigate the perturbation problem for the bounded outer inverse (a bounded linear operator \(S\) is called an outer inverse of a bounded linear operator \(T\) if \(STS=S\)), the bounded \((2,3)\)-inverse and the generalized inverse in Banach spaces. With the help of the generalized Neumann lemma, they also give some new perturbation theorems for the generalized inverse of closed linear operators with respect to certain projectors in Banach spaces and thus extend the corresponding results of \textit{Y.-W.\thinspace Wang} and \textit{H.\,Zhang} [Linear Algebra Appl.\ 426, No.\,1, 1--11 (2007; Zbl 1133.47011)].