Normally solvable operator equations in a Banach space
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.
English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 2, pp 179-192.
Citation Example: Boichuk О. A., Pokutnyi О. О., Zhuravlev V. F. Normally solvable operator equations in a Banach space // Ukr. Mat. Zh. - 2013. - 65, № 2. - pp. 163-174.