Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-24T20:41:16.687Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of barrelledness and related concepts in topological vector spaces

Published online by Cambridge University Press:  20 January 2009

J. O. Popoola  and
I. Tweddle
J. O. Popoola
Affiliation:
University of Lagos, Lagos Nigeria
I. Tweddle
Affiliation:
University of StirlingStirling, FK9 4LA
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.

Let E be a separated locally convex barrelled space with continuous dual E′ and algebraic dual E* and let M be a subspace of E* with and dim Robertson, Tweddle and Yeomans have recently considered the question of barrelledness under the Mackey topology τ(E,E' + M) when E is given to be barrelled under its original topology τ(E,E') [5], [6], [7].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 27 , Issue 3 , October 1984 , pp. 321 - 325
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

REFERENCES

1.Iyahen, S. O.On certain classes of linear topological spaces, Proc. London Math. Soc. 18 (1968), 285–307.CrossRefGoogle Scholar
2.Iyahen, S. O.Semiconvex spaces, Glasgow Math. J. 9 (1967), 111–118.CrossRefGoogle Scholar
3.Popoola, J. O. and Tweddle, I.On the dimension of a complete metrizable topological vector space, Canad. Math. Bull. 20 (1977), 271–2.CrossRefGoogle Scholar
4.Robertson, W. J.Completeness of topological vector spaces, Proc. London Math. Soc. 8 (1958), 242–257.CrossRefGoogle Scholar
5.Robertson, W. J., Tweddle, I. and Yeomans, F. E.On the stability of barrelled topologies, III, Bull. Austral. Math. Soc. 22 (1980), 99–112.CrossRefGoogle Scholar
6.Robertson, W. J. and Yeomans, F. E.On the stability of barrelled topologies, I, Bull. Austral. Math. Soc. 20 (1979), 385–395.CrossRefGoogle Scholar
7.Tweddle, I. and Yeomans, F. E.On the stability of barrelled topologies II, Glasgow Math. J. 21 (1980), 91–95.CrossRefGoogle Scholar
8.Waelbroeck, L.Topological Vector Spaces and Algebras (Lecture Notes in Math., Vol. 230, Springer-Verlag, Berlin and New York, 1971).Google Scholar