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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
Article

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.

Keywords

Banach Space Operator Equation Null Space Inverse Operator Fredholm Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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