2018
Том 70
№ 9

# Solvability criterion and representation of solutions of $n$-normal and $d$-normal linear operator equations in a Banach space

Zhuravlev V. F.

Abstract

On the basis of a generalization of the well-known Schmidt lemma to the case of n-normal and d-normal linear bounded operators in a Banach space, we propose constructions of generalized inverse operators. We obtain criteria for the solvability of linear equations with these operators and formulas for the representation of solutions of these equations.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 2, pp 186-202.

Citation Example: Zhuravlev V. F. Solvability criterion and representation of solutions of $n$-normal and $d$-normal linear operator equations in a Banach space // Ukr. Mat. Zh. - 2010. - 62, № 2. - pp. 167–182.

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