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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 familyof absolutely convex absorbent sets such that
(1) if {nk} is a sequence of positive integers andfor 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, ifand 0 ≤ μk ≤ λkfor each k, then
(i) converges in E[T], and
(ii) for each p.
- 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