TY - JOUR
AU - О. A. Boichuk
AU - V. F. Zhuravlev
AU - О. О. Pokutnyi
PY - 2013/02/25
Y2 - 2023/02/09
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 -