Normally solvable operator equations in a Banach space - Boichuk, О. A.; Zhuravlev, V. F.; Pokutnyi, О. О. (Ukrains’kyi Matematychnyi Zhurnal, 2013)
On the basis of a generalization of the well-known Schmidt lemma to the case of linear, bounded, normally solvable operators in Banach spaces, we propose a procedure for the construction of a generalized inverse for a linear, bounded, normally solvable operator whose kernel and image are complementable in the indicated spaces. This construction allows one to obtain a solvability criterion for linear normally solvable operator equations and a formula for finding their general solutions.