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On the topological dual of a locally convex nuclear space. (English) Zbl 1383.46004

Summary: In this paper, we shall show that an infrabarrelled locally convex nuclear space and a (DF) space are both nuclear if their strong duals are co-nuclear. We shall also show through example that every nuclear space is not co-nuclear and every co-nuclear space is not nuclear. For this, the notion of topological dual of a locally convex space is discussed in Section 1 in order to bring those new results on the topological dual of a locally convex nuclear space as given in Section 2.

MSC:

46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
46A20 Duality theory for topological vector spaces
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