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Subspaces with property (b) in locally convex spaces of quasi-barrelled type

Published online by Cambridge University Press:  24 October 2008

Bella Tsirulnikov
Bella Tsirulnikov
Affiliation:
University of Tel-Aviv, Israel
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A subspace G of a locally convex space E has property (b) if for every bounded set B of E the codimension of G in the linear hull of G ∪ B is finite, (5). Extending the results of (5) and (14), we prove that, if the strong dual of E is complete, then subspaces with property (b) inherit the following properties of E: σ-evaluability, evaluability, the property of being Mazur, semibornological and bornological. We also prove that a dense subspace with property (b) of a Mazur space is sequentially dense, and of a semibornological space – dense in the sense of Mackey (locally dense, following M. Valdivia).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 88 , Issue 2 , September 1980 , pp. 331 - 337
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

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