Ukrainian Mathematical Journal

, Volume 71, Issue 4, pp 537–553 | Cite as

Conditions of Solvability and Representation of the Solutions of Equations with Operator Matrices

  • V. F. ZhuravlevEmail author
  • N. P. Fomin
  • P. N. Zabrodskiy

We propose new methods for the construction of generalized inverse operator matrices for the operator matrices in Banach spaces. The criteria of solvability 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.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • V. F. Zhuravlev
    • 1
    Email author
  • N. P. Fomin
    • 1
  • P. N. Zabrodskiy
    • 1
  1. 1.Zhytomyr National Agricultural-Economical UniversityZhytomyrUkraine

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