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Proceedings of the American Mathematical Society

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Sequential and conditional compactness in the dual of a barrelled space


Author: Edward G. Ostling
Journal: Proc. Amer. Math. Soc. 45 (1974), 123-124
MSC: Primary 46A07
DOI: https://doi.org/10.1090/S0002-9939-1974-0433178-9
MathSciNet review: 0433178
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Abstract: Let $ E$ be a barrelled locally convex space and suppose $ {T_{\mathcal{A}}}$ is a topology on the dual $ E'$ of $ E$ which is admissible for the duality $ (E,E')$. It is shown that each $ {T_{\mathcal{A}}}$ sequentially compact subset of $ E'$ is $ {T_{\mathcal{A}}}$ conditionally compact.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0433178-9
Keywords: Mackey topology, conditionally compact, sequentially compact, barrelled, bornological, admissible topology
Article copyright: © Copyright 1974 American Mathematical Society