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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A closed graph theorem


Author: S. O. Iyahen
Journal: Proc. Amer. Math. Soc. 53 (1975), 165-166
MSC: Primary 46A30
DOI: https://doi.org/10.1090/S0002-9939-1975-0442631-4
MathSciNet review: 0442631
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Abstract: A closed graph theorem is proved, implying that a Hausdorff locally convex space $ E$ need not be barrelled if every closed linear map from $ E$ into $ F$ is continuous, where $ F$ is a reflexive Fréchet or $ LF$-space or a space of distributions.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0442631-4
Keywords: Closed graph theorem, Montel and reflexive spaces
Article copyright: © Copyright 1975 American Mathematical Society