Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0442631
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] D. J. H. Garling, A generalized inductive limit topology for vector spaces, Proc. London Math. Soc. 14 (1964), 1-28. MR 28 #4330. MR 0161121 (28:4330)
  • [2] M. Mahowald, Barrelled spaces and the closed graph theorem, J. London Math. Soc. 36 (1961), 108-110. MR 23 #A2728. MR 0125426 (23:A2728)
  • [3] L. Schwartz, Sur le théorème du graphe fermé, C. R. Acad. Sci. Paris Sér. A-B 263 (1966), A602-A605. MR 34 #6494. MR 0206676 (34:6494)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46A30

Retrieve articles in all journals with MSC: 46A30

Additional Information

Keywords: Closed graph theorem, Montel and reflexive spaces
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society