Geodesic
Some results on solvability of ordinary linear differential equations in locally convex spaces
Sbornik. Mathematics, Tome 71 (1992) no. 1, pp. 29-40 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x=Ax$, $x(0)=x_0$, with respect to functions $x\colon\mathbf R\to E$. It is proved that if $E\in\Gamma$, then $E\times\mathbf R^A\in\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Fréchet spaces, each not isomorphic to $\mathbf R^\infty$, does not belong to $\Gamma$. 
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S. A. Shkarin. Some results on solvability of ordinary linear differential equations in locally convex spaces. Sbornik. Mathematics, Tome 71 (1992) no. 1, pp. 29-40. http://geodesic.mathdoc.fr/item/SM_1992_71_1_a2/

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