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On the three-space-problem for dF spaces and their duals. (English) Zbl 1056.46001

A locally convex space \(E\) is called a dF-space if it is polar semireflexive and it has a fundamental sequence of compact sets. The dual of a Fréchet space \(F\) endowed with the topology of uniform convergence on the precompact subsets of \(F\) is a dF-space. The authors study the three-space problem for duals of barrelled dF-spaces and the duality of short exact sequences of dF-spaces. As the dual of a barrelled dF-space is Fréchet–Montel, the solution to the three-space problems follows from known results.

MSC:

46A04 Locally convex Fréchet spaces and (DF)-spaces
46A03 General theory of locally convex spaces
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