TY - JOUR AU - О. A. Boichuk AU - V. F. Zhuravlev AU - О. О. Pokutnyi PY - 2013/02/25 Y2 - 2024/03/28 TI - Normally solvable operator equations in a Banach space JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 65 IS - 2 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2411 AB - 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. ER -