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Erschienen in:
2020 | OriginalPaper | Buchkapitel
6. Topologies on E″, Quasi-barrelled and Barrelled Spaces
verfasst von : Jürgen Voigt
Erschienen in: A Course on Topological Vector Spaces
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Abstract
The topics of this chapter draw their motivation, with a locally convex space E, from two questions: find topologies on E″ such that the canonical mapping κ: E → E″ is continuous, and investigate properties of topologies on E ensuring that κ is continuous, if E″ is provided with the strong topology β(E″, E′). The first issue leads to the ‘natural topology’ on E″, the second leads to ‘quasi-barrelled’ spaces, and in particular, the answer to the second question motivates the investigation of further related properties of locally convex spaces.