Normally solvable operator equations in a Banach space

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

Abstract

On the basis of a 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 for a linear, bounded, normally solvable operator whose kernel and image are complementable in the indicated spaces. This construction allows one to obtain a solvability criterion for linear normally solvable operator equations and a formula for finding their general solutions.
Published
25.02.2013
How to Cite
BoichukО. A., ZhuravlevV. F., and PokutnyiО. О. “Normally Solvable Operator Equations in a Banach Space”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 2, Feb. 2013, pp. 163-74, http://umj.imath.kiev.ua/index.php/umj/article/view/2411.
Section
Research articles