Abstract: We consider a sequentially complete topological vector space \(Y\) and a linearly invariant family \(\mathcal{E}\) of convex subsets of \(Y\). We say that: \(\mathcal{E}\) has the countable binary intersection property if every countable subfamily of pairwise intersecting sets has a nonempty intersection; a pair \((Y, \mathcal{E})\) is said to admit a countable extension of linear operators if for any separable metrizable topological vector space, its subspace, odd closed-valued upper semicontinuous fan (subadditive positively homogeneous set-valued mapping), and a linear operator defined on the subspace and being a selector of the given fan, there exists a linear selector that extends given linear operator from a subspace to the entire space. The main result states that the pair \((Y, \mathcal{E})\) admits a countable extension of continuous linear operators if \(E\) has the countable binary intersection property. The inverse to this result also holds under the additional assumption that the topological vector space under consideration is locally bounded.
Keywords: fan, extension of linear operators, countable binary intersection property, separability, vector lattice.
Fund name: This study was supported by grant No. 24-71-10094 from the Russian Science Foundation, https://rscf.ru/project/24-71-10094/.
For citation: Kusraeva, Z. A. and Saadulaeva, A. A. On Extension of Linear Selectors, Vladikavkaz Math. J., 2026, vol. 28, no. 1, pp.98-107(in Russian). DOI 10.46698/o1056-6445-9027-m
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