Ukrainian Mathematical Journal

, Volume 65, Issue 2, pp 179–192 | Cite as

Normally solvable operator equations in a Banach space

  • A. A. Boichuk
  • V. F. Zhuravlev
  • A. A. Pokutnyi

On the basis of 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 operator of a linear bounded normally solvable operator whose kernel and image can be complemented in the indicated spaces. The proposed construction enables one to obtain a solvability criterion for linear normally solvable operator equations and a formula for finding their general solutions.


Banach Space Operator Equation Null Space Inverse Operator Fredholm Operator 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • A. A. Boichuk
    • 1
  • V. F. Zhuravlev
    • 1
  • A. A. Pokutnyi
    • 1
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine

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