Hostname: page-component-7f64f4797f-6fdxz Total loading time: 0 Render date: 2025-11-04T02:39:55.389Z Has data issue: false hasContentIssue false
  • English
  • Français

On The Closed Graph Theorem

Published online by Cambridge University Press:  18 May 2009

Alex. P. Robertson  and
Wendy Robertson
Alex. P. Robertson
Affiliation:
The University Glasgow,
Wendy Robertson
Affiliation:
The University Glasgow,
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The closed graph theorem is one of the deeper results in the theory of Banach spaces and one of the richest in its applications to functional analysis. This note contains an extension of the theorem to certain classes of topological vector spaces. For the most part, we use the terminology and notation of N. Bourbaki [1], contracting “locally convex topological vector space over the real or complex field” to “convex space”; here we confine ourselves to convex spaces.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 3 , Issue 1 , December 1956 , pp. 9 - 12
Copyright
Copyright © Glasgow Mathematical Journal Trust 1956

References

REFERENCES

1.Bourbaki, N., Espaces vectoriels topologiques, Actualités Scientifiques et Industrielles no. 1189, Paris, Hermann, 1953 and no. 1229, Paris, Hermann, 1955.Google Scholar
2.Collins, H. S., Completeness and compactness in linear topological spaces, Trans. Amer. Math. Soc., 79 (1955), 256–280.CrossRefGoogle Scholar
3.Dieudonné, J., et Schwartz, L., La dualité dans les espaces (ℱ) et (ℒℱ), Ann. Inst. Fourier Grenoble 1 (1950), 61–101.CrossRefGoogle Scholar
4.Grothendieck, A., Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16, 1955.Google Scholar
5.Pták, V., On complete topological linear spaces, Čehoslovach Mat. Ž. 3 (78) (1953), 301–364.Google Scholar