Perturbation analysis for oblique projection generalized inverses of closed linear operators in Banach spaces
The authors consider a perturbation analysis for oblique projection generalized inverses of closed linear operators in Banach spaces. Let \(X\) and \(Y\) be two Banach spaces and let \(C(X,Y)\) and \(B(X,Y)\) denote the homogeneous set of all closed linear operators and the Banach space of all bounded linear operators from \(X\) into \(Y\), respectively. For \(T\in C(X,Y)\) with a closed range \(R(T)\) and a dense domain, the authors define the oblique projection generalized inverse \(T^+\in B(Y,X)\) of \(T\) in a similar way to the Moore--Penrose inverse. The main result in the paper is an explicit expression of the oblique projection generalized inverse \(T^+\) of a closed linear operator \(T\in C(X,Y)\) and an error estimate under \(T\)-bounded perturbation of \(T^+\).
scientific article; zbMATH DE number 5190755