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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 2, pp. 163–174, February, 2013.
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Boichuk, A.A., Zhuravlev, V.F. & Pokutnyi, A.A. Normally solvable operator equations in a Banach space. Ukr Math J 65, 179–192 (2013). https://doi.org/10.1007/s11253-013-0772-z
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DOI: https://doi.org/10.1007/s11253-013-0772-z