Abstract
Two known definitions of regularizability for topological vector spaces are found to be equivalent. Regularizability in the sense of Tikhonov is considered in reflexive linear metric spaces. In particular, an example is presented of a linear continuous injective operator on a reflexive Frécnet space whose inverse cannot be regularized. The latter indicates the sharp difference between regularizability in Fréchet spaces and in Banach spaces, respectively.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 6, pp. 777–781, June, 1990.
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Menikhes, L.D., Plichko, A.M. Theory of regularizability in topological vector spaces. Ukr Math J 42, 686–689 (1990). https://doi.org/10.1007/BF01058913
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DOI: https://doi.org/10.1007/BF01058913