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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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