Hostname: page-component-7479d7b7d-c9gpj Total loading time: 0 Render date: 2024-07-11T08:33:32.147Z Has data issue: false hasContentIssue false
  • English
  • Français

On quasi-normable echelon spaces

Published online by Cambridge University Press:  20 January 2009

M. Valdivia
M. Valdivia
Affiliation:
Facultad de MatemáticasDr Moliner, s/nBurjasot, Valencia, Spain
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.

In this paper we prove that if the strong dual of an echelon space fulfils the Mackey convergence condition the echelon space is quasi-normable. Also we give a characterisation of the quasi-normable echelon spaces and we deduce that every non-quasi-normable echelon space is the strong dual of a non-complete (LB)-space.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 24 , Issue 1 , February 1981 , pp. 73 - 80
Copyright
Copyright © Edinburgh Mathematical Society 1981

References

REFERENCES

(1)Grothendieck, A., Sur les espaces (F) et (DF), Summa Brasil, Math. 3 (1954) 57–123.Google Scholar
(2)Komura, T. and Komura, Y., Sur les espaces parfaits de suites et leurs généralisations, J. Math. Soc. Japan 15 (1963) 319–338.Google Scholar
(3)Köthe, G., Topological Vector Spaces I (Springer-Verlag, Berlin-Heilelberg-New York, 1969).Google Scholar
(4)Valdivia, M., Algunas propiedades de los espacios escalonados, Rev. Real Acad. Ciencias, Madrid, 73 (1979) 389–400.Google Scholar
(5)Warner, S., The topology of compact convergence on continuous functions spaces, Duke Math. J. 25 (1958) 265–282.CrossRefGoogle Scholar