A closed graph theorem
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- by S. O. Iyahen PDF
- Proc. Amer. Math. Soc. 53 (1975), 165-166 Request permission
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.References
- D. J. H. Garling, A generalized form of inductive-limit topology for vector spaces, Proc. London Math. Soc. (3) 14 (1964), 1–28. MR 161121, DOI 10.1112/plms/s3-14.1.1
- M. Mahowald, Barrelled spaces and the closed graph theorem, J. London Math. Soc. 36 (1961), 108–110. MR 125426, DOI 10.1112/jlms/s1-36.1.108
- Laurent Schwartz, Sur le théorème du graphe fermé, C. R. Acad. Sci. Paris Sér. A-B 263 (1966), A602–A605 (French). MR 206676
Additional Information
- © Copyright 1975 American Mathematical Society
- 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