Geodesic
On Dominated Extension of Linear Operators
Matematičeskie zametki, Tome 108 (2020) no. 2, pp. 190-199

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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.
Keywords: ordered topological vector space, reproducing cone, normal cone, separability, $\sigma$-interpolation property, linear operator, dominated extension, axiom of countable choice. 
@article{MZM_2020_108_2_a3,
     author = {A. A. Gelieva and Z. A. Kusraeva},
     title = {On {Dominated} {Extension} of {Linear} {Operators}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {190--199},
     publisher = {mathdoc},
     volume = {108},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_108_2_a3/}
}
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A. A. Gelieva; Z. A. Kusraeva. On Dominated Extension of Linear Operators. Matematičeskie zametki, Tome 108 (2020) no. 2, pp. 190-199. http://geodesic.mathdoc.fr/item/MZM_2020_108_2_a3/