Abstract
An ordered topological vector space has the countable dominated extension property if any linear operator ranging in this space, defined on a subspace of a separable metrizable topological vector space, and dominated there by a continuous sublinear operator admits extension to the entire space with preservation of linearity and domination. Our main result is that the strong \(\sigma\)-interpolation property is a necessary and sufficient condition for a sequentially complete topological vector space ordered by a closed normal reproducing cone to have the countable dominated extension property. Moreover, this fact can be proved in Zermelo–Fraenkel set theory with the axiom of countable choice.
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Gelieva, A.A., Kusraeva, Z.A. On Dominated Extension of Linear Operators. Math Notes 108, 171–178 (2020). https://doi.org/10.1134/S0001434620070184
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DOI: https://doi.org/10.1134/S0001434620070184