Singh, Abhik On the topological dual of a locally convex nuclear space. (English) Zbl 1383.46004 Aligarh Bull. Math. 33, No. 1-2, 15-18 (2014). 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 Keywords:locally convex space; dual; locally convex nuclear space; infrabarrelled; strongly bounded; (DF) spaces; equi-continuous; boundedly summable; co-nuclear space PDFBibTeX XMLCite \textit{A. Singh}, Aligarh Bull. Math. 33, No. 1--2, 15--18 (2014; Zbl 1383.46004)