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Topological vector space with a locally convex topology, i.e. induced by a system of seminorms.
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Extension of Valdivia-Vogt isomorphism from $\mathscr{D}(K)$ to $\mathscr{E}'(K)$
This is just an addendum to the above answers so really a comment but too long--I hope that it will be of interest. At first, there is an abstract construction which associates to each self adjoint, …