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When $$(E,\sigma{}(E,E'))$$ is a $$DF$$-space? (English) Zbl 0782.46006
The authors give an elementary proof of the following: For a Hausdorff locally convex space $$E$$, either $$(E,\sigma(E,E'))$$ or $$(E',\sigma(E',E))$$ is a $$DF$$-space if and only if $$E$$ is finite- dimensional. For an infinite-dimensional Banach $$E$$, the result that neither $$(E,\sigma(E,E')$$ or $$(E',\sigma(E',E))$$ is a $$DF$$-space, is due to S. Radenović [Publ. Inst. Math., Nouv. Ser. 44(58), 155-157 (1988; Zbl 0684.46003)].
##### MSC:
 46A20 Duality theory for topological vector spaces 46A03 General theory of locally convex spaces
##### Keywords:
$$DF$$-space
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