Some results on solvability of ordinary linear differential equations in locally convex spaces

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Abstract

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 $x: R\to E$. It is proved that if $E\in \Gamma$, then $E\times R^A$ is-an-element-of $\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to $\omega$, does not belong to $\Gamma$.
Original languageEnglish
Pages (from-to)29-40
Number of pages12
JournalSbornik Mathematics
Volume71
Publication statusPublished - 1992

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