Metric generalized inverse for linear manifolds and extremal solutions of linear inclusion in Banach spaces (Q1763800)

The central problem that originally motivated this paper is related to the characterization and construction of all extremal solutions of a linear inclusion \(y\in M(x)\), where \(M\) is a linear manifold in \(X\times Y\) (\(X\) and \(Y\) are Banach spaces). The main result of the paper concerns the characterization of the set of all extremal or least extremal solutions in terms of metric operator parts and metric generalized inverses of linear manifolds in Banach spaces. The proofs rely essentially on the generalized orthogonal decomposition theorem in Banach spaces.