2017
Том 69
№ 6

All Issues

Normally solvable operator equations in a Banach space

Boichuk A. A., Pokutnyi A. A., Zhuravlev V. F.

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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.

English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 2, pp 179-192.

Citation Example: Boichuk A. A., Pokutnyi A. A., Zhuravlev V. F. Normally solvable operator equations in a Banach space // Ukr. Mat. Zh. - 2013. - 65, № 2. - pp. 163-174.

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