Geodesic
On~a~dual problem. I.~General results. Applications to Fr\`echet spaces
Sbornik. Mathematics, Tome 26 (1975) no. 2, pp. 181-212

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Let $H$ be a separated locally convex space; $x_k\in H$, $x_k\ne0$, $k=1,2,\dots$ . The author shows that if $H$ is a Frèchet space or an $LN^*$-space, then the system $\{x_k\}$ is a basis (topological or absolute) in the closure of its linear span if and only if the system of equations $\varphi(x_k)=d_k$, $k=1,2,\dots$, has a solution $\varphi$ in $H'$ for any sequence $\{d_k\}$ from a certain space $E_1$ (respectively, from $E_2$ for an absolute basis). Bibliography: 32 titles. 
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     author = {Yu. F. Korobeinik},
     title = {On~a~dual problem. {I.~General} results. {Applications} to {Fr\`echet} spaces},
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     number = {2},
     year = {1975},
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Yu. F. Korobeinik. On~a~dual problem. I.~General results. Applications to Fr\`echet spaces. Sbornik. Mathematics, Tome 26 (1975) no. 2, pp. 181-212. http://geodesic.mathdoc.fr/item/SM_1975_26_2_a2/