Abstract
For a topological vector space (X, τ), we consider the family LCT(X, τ) of all locally convex topologies defined on X, which give rise to the same continuous linear functionals as the original topology τ. We prove that for an infinite-dimensional reflexive Banach space (X, τ), the cardinality of LCT(X, τ) is at least \( \mathfrak{c} \).
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 94, Proceedings of the International Conference “Lie Groups, Differential Equations, and Geometry,” June 10–22, 2013, Batumi, Georgia, Part 1, 2014.
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Martín-Peinador, E., Tarieladze, V. On the Set of Locally Convex Topologies Compatible with a Given Topology on a Vector Space: Cardinality Aspects. J Math Sci 216, 577–579 (2016). https://doi.org/10.1007/s10958-016-2917-8
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DOI: https://doi.org/10.1007/s10958-016-2917-8