Conditions of solvability and representation of the solutions of equations with operator matrices

  • V. F. Zhuravlev
  • P. N. Zabrodskiy
  • N. P. Fomin

Abstract

We propose new methods for the construction of generalized inverse operator matrices for the operator matrices in Banach spaces. The solvability criteria and the formulas for representations of the general solutions of operator equations with operator matrices are obtained. As an application, we consider the relationship between the obtained formulas and the well-known Frobenius formula for the construction of the matrix inverse to a nondegenerate block matrix.
Published
25.04.2019
How to Cite
ZhuravlevV. F., ZabrodskiyP. N., and FominN. P. “Conditions of Solvability and representation of the Solutions of Equations With Operator Matrices”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 4, Apr. 2019, pp. 471-85, http://umj.imath.kiev.ua/index.php/umj/article/view/1452.
Section
Research articles