Abstract
We provide an exhaustive description of the class of locally convex spaces in which all Archimedean cones are closed. We introduce the notion of quasidense set and prove that the above class consists of all finite-dimensional and countable-dimensional spaces \( X \) whose topological dual \( X^{\prime} \) is quasidense in the algebraic dual \( X^{\#} \) of \( X \).
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Funding
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0004).
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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 5, pp. 945–970. https://doi.org/10.33048/smzh.2023.64.505
The article is dedicated to Anatoly G. Kusraev on the occasion of his 70th birthday.
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Gutman, A.E., Emelianenkov, I.A. Locally Convex Spaces with All Archimedean Cones Closed. Sib Math J 64, 1117–1136 (2023). https://doi.org/10.1134/S0037446623050051
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DOI: https://doi.org/10.1134/S0037446623050051