Abstract
The main result states that if E is a separable Fréchet lattice and F is a (locally solid) topological vector lattice with the σ-interpolation property then each positive linear operator T0 from a majorizing subspace G ⊂ E into F admits extension to a continuous positive linear operator T from E into F. This fact is proved by using only the axiom of countable choice.
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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 2, pp. 330–336.
The authors were supported by the Russian Foundation for Basic Research (Grant 18-31-00205).
The authors are grateful to the referee for constructive remarks and comments.
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Ilina, K.Y., Kusraeva, Z.A. Extension of Positive Operators. Sib Math J 61, 261–265 (2020). https://doi.org/10.1134/S0037446620020081
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DOI: https://doi.org/10.1134/S0037446620020081