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Proceedings of the American Mathematical Society

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On a characterization of barrelled spaces


Author: A. Wilansky
Journal: Proc. Amer. Math. Soc. 57 (1976), 375
MSC: Primary 46A07
DOI: https://doi.org/10.1090/S0002-9939-1976-0412761-2
MathSciNet review: 0412761
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Abstract: We prove that a l.c. space $ E$ is barrelled if every closed graph linear map: $ E \to C(X)$ is continuous; $ X$ compact $ {T_2}$. This generalizes Mahowald's criterion, but the main contribution is the simplicity of the proof.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0412761-2
Article copyright: © Copyright 1976 American Mathematical Society