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Lifting convergent sequences with networks
Published online by Cambridge University Press: 24 October 2008
Extract
Definition (Moukoko Priso(2)). A locally convex spaceE[T] is said to have a strict absorbent network of type Σ if there exists in E a family
of absolutely convex absorbent sets such that
(1) if {nk} is a sequence of positive integers and
for each k, then the series
converges in E[T]
(2) for each sequence {nk} there is a sequence {λk} of positive real numbers such that, if
and 0 ≤ μk ≤ λkfor each k, then
(i) 
converges in E[T], and
(ii) 
for each p.
Information
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 1 , July 1971 , pp. 27 - 30
- Copyright
- Copyright © Cambridge Philosophical Society 1971
References
REFERENCES
(1)Husain, T.The open mapping and closed graph theorems in topological vector spaces (Oxford, 1965)CrossRefGoogle Scholar
(2)Moukoko Priso, P.Sur les questions de relèvement de suites convergentes. C.R. Acad. Sci., Paris, Sér. A 269 (1969), 1063–1065.Google Scholar
(3)de Wilde, M.Réseaux dans les espaces linéaires à semi-normes. Mem. Soc. Roy. Sci. Liège 17 (1969).Google Scholar