TY - JOUR
AU - V. F. Zhuravlev
AU - P. N. Zabrodskiy
AU - N. P. Fomin
PY - 2019/04/25
Y2 - 2020/11/28
TI - Conditions of solvability and representation
of the solutions of equations with operator matrices
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 71
IS - 4
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1452
AB - We propose new methods for the construction of generalized inverse operator matrices for the operator matrices in Banachspaces. The solvability criteria and the formulas for representations of the general solutions of operator equations withoperator matrices are obtained. As an application, we consider the relationship between the obtained formulas and thewell-known Frobenius formula for the construction of the matrix inverse to a nondegenerate block matrix.
ER -