Abstract
We introduce a new concept of generalized solution of operator equations with closed linear operator in a Banach space as an element of the completion of the space in certain locally convex topology. We prove a theorem on the existence and uniqueness of a generalized solution and give examples of finding the generalized solution for infinite systems of the linear algebraic equations.
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References
N. Bourbaki,Éléments de Mathématique. Premiere Partie. Les Structures Fondamentales de L'Analyse. Livere V. Espases Vectoriels Topologiques [Russian translation], Inostrannaya Literature, Moscow (1959).
S. G. Krein (editor),Functional Analysis [in Russian], Nauka, Moscow (1972).
Yu. M. Berezanskii,Expansion of Self-Adjoint Operators in Eigenfunctions [in Russian], Naukova Dumka, Kiev (1965).
Additional information
Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 48, No. 9. pp. 1286–1290, September, 1996.
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Petunin, Y.I. On the concept of generalized solution of operator equations in banach spaces. Ukr Math J 48, 1460–1464 (1996). https://doi.org/10.1007/BF02595365
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DOI: https://doi.org/10.1007/BF02595365